Lots of good ideas. I would say don't make this one a power struggle. Right now more than anything you should be trying to establish a good habit, not create a bad image around the idea of tooth brushing.
With that said, three year olds are wanting to be independent at least mine does. Sometimes all it takes for us is that the tooth brushing is his idea. Sometimes it is the choice of which toothbrush he uses (he has 3--electric, one with a firefly-type flashing end and his original toddler toothbrush.
Then I do my turn, your turn. Which means he takes a turn at trying to brush his teeth, then mommy takes a turn.
Also, he learned a song about a pet gorilla named matilda who sings "EE EE EE OO OO OO EE EE EE OO OO OO" etc. and I have him make those sounds and the ahh sound while we're brushing--good ways to get oral motor going on while getting the teeth clean.
Hope these suggestions and the others help out.