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 $a+b$ .