We're Only On Coprime Numbers?

Geometry Level 5

Evaluate

P=ksin(kπ2016)\large P=\prod_{k}\sin\left(\dfrac{k\pi}{2016}\right)

where the product is taken over all kk with 1k10081\leq k\leq 1008 and gcd(k,2016)=1\gcd(k,2016)=1.

Write your answer in the form P=a2bP=\dfrac{a}{2^b}, where aa and bb are integers, and aa is odd. Enter a+ba+b.

Clariifcation: gcd() \gcd(\cdot) denotes the greatest common divisor function.


Inspiration.

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