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.
Sorry, this was my first post and I wasn't sure where to put it! I can assure you though, that this was not a homework question, instead it was just my curious self doing physics for fun. Questions like this have been asked before on this site but not looking for theta, so I thought I would post so others and myself could understand it.
Anyways, thanks for the response. It's so tempting to just divide by infinity that I didn't even consider that tangent(90) approaches infinity. I guess I'm getting lazy and need to brush up on my calculus.
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