Fibonacci Product

$\large \prod_{n=2}^\infty \left(1-\dfrac{2}{F_{n+1}^2-F_{n-1}^2+1}\right)$

Let $F_n$ denote the $n$ th Fibonacci number , $F_0 = 0, F_1 = 1$ and $F_n = F_{n-1} + F_{n-2}$ where $n=2,3,4,\ldots$ .

If the product above is equal to $\dfrac AB$ , where $A$ and $B$ are coprime positive integers, find $A+B$ .