Happy Bday Trevor B! (a bit late may be)

Calculus Level 3

\[\large \int_{1729}^{2016} \dfrac{1-\cos(2x)+2\sin^2(x)\cos(2x)}{\sin^2(x)\cos^2(x)} dx = \ ?\]


This problem is original and is dedicated to Trevor B on his birthday! :)
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