Power of Four and Sine Summation

Geometry Level 5

n=14nsin4(π2n)\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 πab\dfrac{\pi^a}b, where aa and bb are positive integers, find the value of a+ba+b.

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