Fun with 2015 and 2016!!

Calculus Level 4

\[\displaystyle \int_{ - \pi /2}^{\pi /2} \dfrac1{2015^{x} + 1}\cdot \dfrac {\sin^{2016}x}{\sin^{2016}x + \cos^{2016}x} \, dx = \, ? \]

Give your answer up to 3 decimal places

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