This looks suspiciously like a homework problem. In any event, it is close enough to a typical homework problem that it should have been posted in the homework forum. Please consider doing that next time.
Regarding what you did wrong, the limit of the first term is not zero. If theta goes to 90 degrees, tan of theta is infinite also. If you hadn't divided by omega squared, you would have seen immediately that, in the limit of infinite omega, tan theta becomes infinite, and that theta approaches 90 degrees.
Chet