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$\mathscr{E} = \displaystyle \int_{0}^{\pi/2} \sqrt{1- \sin(2016 x) }\, dx$

Find $\mathscr{E}.$

Inspiration

Bonus: Generalize for $\displaystyle \int_{0}^{\pi/2} \sqrt{1- \sin(12n x) }\, dx$, where $n$ is a positive integer, and prove it.

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