M.G.
I would say this is definitely part of her age, but that doesn't mean it isn't annoying and inappropriate. I have found that when my own (three-year-old) daughter throws such a fit, it usually means she's feeling like she hasn't received enough attention. When she gets out of control, the best thing I can do is leave the room for awhile. That's definitely not what she's looking for, or what she wants me to do, but she gets the idea that yelling and screaming is not the way to get what she wants. When she finally calms down and we can talk reasonably, I'll come back in and tell her, "Let's try again." Usually by then she's ready to. She goes through stages where we she won't throw a tantrum for months, then all of a sudden it'll flare again, and I've found that it's usually when I've become distracted with too many other things to do and haven't been giving her the time she needs. We tend to get to a point where I'm just dragging her along with me where ever I need to go, instead of doing things with her. So when she starts throwing tantrums, I know I need to work on my own life a little as well. I try to clear out my schedule a little and spend a bit of extra time with her (when she's calm, that is) and, eventually, the tantrums go away.
Along with all that, I try to praise her for doing good things. When she's at her worst, it's hard to find anything to praise, but that's when she needs to hear it the most, so look hard. I have seen a lot of kids when they get older rejecting what their parents tell them, because they are always being criticized and never praised. If my daughter doesn't learn anything else from me, I want her to know that it's worth trying to do what's right and that even when she makes mistakes, her parents still love her. This is probably stuff that you already know, but I know how you feel. It's just nice to know you're not the only one dealing with it. Good luck!