Expo-Trig equation

Geometry Level 3

$\large 81^{\sin^2{x}} + 81^{\cos^2{x}} = 30$

If $A$ and $B$ are the two values of $x \in \left[0, \frac{\pi}{2}\right]$ such that the equation above is fulfilled, find the value of $\dfrac{\pi}{A+B}$ .