Calculus to Combinatorics

Calculus Level 4

\[\large \displaystyle \dfrac{1}{\pi}\int_0^{{\pi} / {2}}\left (\dfrac {\sin 2 \theta}{\cos \theta}\right)^{2016} \, d\theta \]

If the value of the integral above is equal to \(\dbinom {2n+1}{n} \), find the value of \(2n+2\).

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