Just a note of solidarity - my daughter (now nearly 4) went through a terrible aggressive phase just after 2 and again just after 3.
She was a biter, a pincher, a hitter and a kicker - both at home and at nursery.
At home we could moderate it, but at nursery (despite the fact it's a great nursery, and the fact she loves it) - we'd sometimes pick her up and they'd have up to 7 incident reports, from where she'd been on a biting rampage.
We just didn't know what to do: we expect good behaviour, we explain things, we're firm, we model good behaviour (we're not even a remotely aggressive family, physically or verbally, we're a calm bunch).
She just has a really short fuse. And it seemed to be amplified when she was going through some sort of change, either in her circumstances (like moving rooms at nursery), or in herself (just on the brink of speaking, just on the brink of potty training etc.).
There were times we really wondered if there was something 'wrong' with her, or if we were doing something wrong.
Now she's a little bit older, she is getting better at moderating her behaviour - so we work with her on that, giving her ways of catching herself before she responds aggressively, giving her pre-set sentences to use to express her annoyance (the book 'Teeth are not for Biting' came in handy, often).
All through this, even in her most aggressive phases she was intrinsically a lovely kid - 70-80% of the time: smart, sociable, kind - just so quick to anger, and had no way of expressing her annoyance without resorting to flailing limbs and snappy jaws.
It will pass. Be firm. Be kind (I found parenting as if Supernanny was watching a good tactic to make sure I was handling it like an adult, rather than getting frustrated). And do know that perfectly nice kids can be monstrously aggressive - and they're still nice kids, we just need to ease them through that phase until they're borderline reasonable.