How can I be sure that 1 + csc2 θ - cot2 θ is simplified?

Ok, so the only way that I found to start simplifying is to use the Pythagorean Identity of 1 + cot2 θ = csc2 θ. Knowing this relation between csc and cot, I'm wildly guessing that i can divide by cot in every item. 1 / cot2 θ + csc2 θ / cot2 θ - cot2 θ / ot2 θ. This results in tan2 θ + csc2 θ / cot2θ - 1. Can this be done? If it can, is it right? If not, how to correctly simplify this expression?