My first problem on Brilliant

Calculus Level 5

\( \large \displaystyle\int_{0}^{\pi/2} \ln ( \cos (x)) \ln( \sin (x) ) \sin (2x) dx\).

Evaluate the above integral. If your answer comes in form of \(\dfrac ab - \dfrac{\pi^c}{d}\), where \(\gcd (a,b) =1\). Then find \(a+b+c+d\).

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