Who's up to the challenge? 36

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

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

Note :the fraction is in simplest terms