Pray for patience. I am a survivor of a major tantrum thrower, she started at about the same age. She is 8 1/2 yrs old now. You didn't mention if anything triggered her tantrums or not, but my daughter's happened when things did not go her way (the cause of a lot of tantrums)and seemed to be more about controlling her environment. There are 3 things that worked for me, and none of them had a 100% success rate, that's why there are 3 main ones, and sometimes none of them worked and we had to wait it out.
1. Ignore it. Don't look, don't respond, don't talk, just go about your activity. If she hangs on you, firmly (but not rough) remove her and walk away. Do not respond except by calmly saying something like "I can't understand you when you scream like that, when you can tell me in a regular voice I will talk to you", but don't say it over and over, and you have to remain calm and pleasant (easier said than done I know). If she is non-verbal,keep it short. "we don't scream" or even "no screaming" or even "hurts Mommy's ears". When the tantrums ends (and they all eventually do)I would say something like, "I'm glad you can talk to me now, are you sad? (or mad, whatever) why are you sad? (helps her identify her feelings)" Usually when she was on my lap. Again, if she is not verbal, you may have to help her. "are you mad about no ice cream?" and give suggestions. Then explain (shortly) "I can see why you would be mad about that, it must be frustrating not to have ice cream when you want it(validates her feelings)but in our house (I often used family)we don't have ice cream right before supper (gives the rule/reason and also it lays the blame on "the rules" instead of you)now would you like to have your ice cream for dessert or after your bath?" (Gives her control and teaches decision making) Praise her choice and for talking to you. ("In this family we like to talk about our problems"). I taught pre-school for 5 years and we often used this method in the classroom. Negative actions do not get attention, while positive actions get positive reinforcement, plus helping them identify, understand and deal with their emotions and give them some control in making decisions. *Side note: while ignoring the tantrum, do something that she finds interesting or enjoys doing. It worked a lot of the time with my daughter. I would start cooking (she loved to "help mix") or pick flowers. Sometimes I would pick up one of her books and read it, or color with her crayons,play with her dolls. Usually it would cut the tantrum short and she would wander over to see what I was doing and her need to play with me or her curiosity would win out over the tantrum. Yes, it takes a lot of time this way.
2. Give her a safe place to "get it all out" where she can't hurt herself, in our house it was the bathroom rug. (no sharp corners, objects etc)when she would get up if she wasn't calm, I would put her back on it and tell her when she was calm she could come out. (at your daughter's age I did not leave her alone, I just sat, usually reading or trying to) as she got older, she would seek out the bathroom and carry on, when she was done she would just come out. Now her bedroom is her "safe zone". She still has the occasional fit, and we tell her to go to her room and get it all out. When she's done, she'll usually come out and talk.
3. If you see a tantrum coming, try to short circuit it. If its a reaction to not getting her way, give her another choice. "Would you like to play with the doll or the truck?" "Would you like peas or beans?"The more control you can give her about things that don't really matter, the better. That way, on the things that count, it will make a real difference. My son is 12 and I really think because we let him make a lot of his own choices he handles rules and reasoning well. Since we let him have control over things that don't really matter (his clothes, his hair, his room) when we say no, there is a good reason for it, and we give him the reason. 95% of the time he accepts it, no questions asked. A lot of our tantrum throwers at pre-school were the children of parents who never let them do anything on their own and micro-managed everything in their child's life, they were never able to make descisions on their own! Kids want to be independant and if all they are hearing is "no" all the time, they will act out.
I don't know about your daughter, but my daughter is very emotional and I think that personality contrbuted to her tantrums, she's hot and cold, never lukewarm. But the very fire in her that caused her tantrums is the same fire that drives her to stand up to bullies, be great on the soccer field, and have a the confidence to stand up for what she believes in, be herself, and not give in to peer pressure. She has a heart as big as her temper. She has mellowed with age, but it is normal for kids to have tantrums into 4 and 5 years old, so hang in there!
PS, my mother in law said my husband used to throw tantrums so bad he would pass out too. My Ped. said they either hyperventilate from crying and breathing in and out rapidly or exhaust their "out breath" from screaming and don't breathe in fast enough. In either case when they "pass out" they automatically start beathing normally on their own and wake up.