# Who's up to the challenge? 36

Geometry Level 5

$\large \displaystyle\sum _{ n=1 }^{ 2015 }{ (-1)^{ n }\sin ^{ 2016 }{ \left( \dfrac { n\pi }{ 2016 } \right) } } =\dfrac { a }{ { 2 }^{ b } }$

The equation above holds true for positive integers $$a$$ and $$b$$ with $$b$$ maximized. Find $$a+b$$.

Note:the fraction is in simplest terms

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