If m^{2}(\sin \theta-1)+n^{2}(\sin \theta+1)=0, where 0\lt \theta\lt \frac{\pi}{2}, then what is (m^{2}+n^{2})\cos \theta-(m^{2}-n^{2})\cot \theta equal to?

Explanation

Rearranging gives \sin\theta = \frac{m^2-n^2}{m^2+n^2}. Using a right triangle, the base is 2mn, so \cos\theta = \frac{2mn}{m^2+n^2} and \cot\theta = \frac{2mn}{m^2-n^2}. Substituting these in the target expression yields 2mn - 2mn = 0.

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