# 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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