# We're Only On Coprime Numbers?

Geometry Level 5

Evaluate

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

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

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

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

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