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 \(\dfrac{\pi}{A+B}\).

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