I'd have to agree with the other posters that have said you need to see some one about this situation. Medical or not, it sounds like a therapist for the whole family may be in order if for no other reason than to make sure everyone learns some communication skills and is required to listen to each-other.
I have experienced kids that throw tantrums at this age that did so because there were evident behavioral and/or emotional disorders and the challenges that go with them having been a teacher at a school for kids with disabilities such as severe ADHD, Bi-polar disorder, Aspberger's, and Tourette's Syndrome to name a few, but I've also known kids that throw tantrums simply because they work. Many times both situations applied for my students. For all of these kids, the most helpful thing was to teach them with patience and understanding and firm limits.
There are three parts to successfully eliminating a tantrum habit.
The first part of calming kids is letting them know you hear their beef. Learn how to paraphrase your daughter so she knows you understand her. Getting in touch with a therapist will help you do this as well as set you down a path toward resolving any latent angers or fears either of you are holding toward the other.
The Second part is in developing calming skills for the child. This is also an area where having an expert around will be of great service to you. You are a parent at your wits end and you need some help too. There are a host of techniques that can be used, special breathing, visualizing, counting, squeezing a ball. . . which technique is best for your kid will depend on your kid and her particular make up. Is there an underlying chemical element? if so, there are also medications that can help though they won't eliminate behaviors entirely. Only a trained professional can help you with this. I was not one of these, but as a teacher of kids that needed the extra help, I had access to one when one was needed for a student and they can truly work wonders.
Finally, it is super important not to get so lost in understanding your daughter that you don't also set a boundaries for her behavior. I always have, and probably always will, refused to converse or engage with a kid in the middle of the tantrum. Calmly but firmly saying something like, "I can't understand you while you are screaming. Come talk to me when you've calmed down." Is one way to set this limit on her behavior. If your daughter knows and trusts you will listen when she is calm, she is more likely to calm down more quickly. If she hasn't already been diagnosed with some disorder, chances are that even if there is an underlying ailment, she can still learn better ways to express her frustrations and angers and she'll need you to set stern limits and consistently stick to those limits in order to learn that her temper tantrums won't work. Again, a professional can be helpful in advising you in this area as well. If there isn't some underlying disorder, a family therapist can still be a critical part of your team for achieving more family peace.