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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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