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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