The Trouble Of Squared Sines

Calculus Level 5

\[ \large\sum_{n=1}^\infty \dfrac{\sin^2 \left( \frac{n\pi}{12}\right) \sin^2 \left(\frac{n\pi}{16}\right) }{n^2} \]

If the series above is equal to \( A\times \pi^B\) for rational numbers \(A\) and \(B\), find the value of \(B\div A\).

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