Tricky 2015 Sum

Calculus Level 3

$\displaystyle\sum_{n=0}^{\infty} \dfrac{1}{2015^{2^{n}} - 2015^{-(2^{n})}}$

If the closed form of the series above is in the form $\frac a b$ , where $a$ and $b$ are positive coprime integers, then find $b - a.$