# Power of Four and Sine Summation

Geometry Level 5

$\large\displaystyle\sum_{n=1}^{\infty}4^n\sin^4\left(\dfrac{\pi}{2^n}\right)$

If the value of the summation above is in the form of $\dfrac{\pi^a}b$, where $a$ and $b$ are positive integers, find the value of $a+b$.

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