# Back to the Roots

Geometry Level 5

$\prod_{k=1}^{(n+1)/2}\left(1+8\sin^2\left(\frac{(2k-1){\pi}}{2{n}}\right)\right)$ for odd $$n$$ can be written as $$ab^n+c$$, where $$a,b,c$$ are positive integers. Find $$a+b+c$$.

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