Identities?

Geometry Level 3

The smallest positive solution of the equation \[2 \sin^2 3x - \cos 8x - 1 = 0\] in the interval \(\left( 0, \frac{\pi}{2}\right)\) can be expressed in the form \(\frac{a\pi}{b}\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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