The definite integral!

Calculus Level 5

\(\displaystyle\int_0^{\frac{\pi} {2}} \ln \left(\dfrac{\ln^2 \sin\theta} {\pi^2+\ln^2\sin\theta} \right) \dfrac{\ln \cos\theta} {\tan\theta} \ d\theta =\dfrac{\pi^a} {b} \)

Find \(a+b\)

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