C.,
when my son started doing that sort of thing at age 3, I figured that B.F. Skinner, the infamous behaviorist, knew something, so I put some behaviorist psychology to work. What I did was to first make sure that he was not putting himself in physical danger, and then just walked out of the room and TOTALLY ignored his tantrum. It worked. He threw about three tantrums, saw that they didn't get him what he wanted, and stopped throwing tantrums. He has never had a tantrum since (he is now 26).
The theory behind this (operant conditioning) is as follows: People choose behavior based upon environmental responses to their behaviors. If the environmental response is what the person wants, he will persist in the behavior to get more of the response (i.e., the behavior is reinforced). If the response is not what he wants, he will stop doing the behavior (i.e., the behavior will be extinguished). In my son's case, he was tantrumming to get some response from me. If I gave him what he wanted, I would have reinforced his behavior and guaranteed that he would do it again the next time he wanted something. Even if he didn't get what he was demanding, any response, even negative, on my part, might have reinforced his behavior. So,if I got all upset, he might conclude that my response was very entertaining and continue tantrumming the next time he got bored or wanted something. The way to extinguish the behavior was to not reinforce it at all, i.e., to totally, flat-out ignore it.
Behaviorist theory worked on this issue in my son's case. You might try it for your daughter.
Just a caution, though. Intermittent reinforcement can make a behavior nearly impossible to extinguish. If you ignore the bad behavior some of the time and reinforce it even once or twice, you have created a monster. She will do it again and again even in the absence of reinforcement because you reinforced it once or twice a long time ago. So, consistency and control of your emotions are key to success with this method. (Illustration of intermittent reinforcement: slot machines) Do not embark on the use of behaviorist theory if you are not going to be totally consistent in refusing to reinforce her behavior.
Good luck. This is not fun. It is, however, part of the territory in dealing with a small child.
Linda