Really Simple Integral?

Calculus Level 5

0π2ln2(sin(x))dx=π3a+πbln2(c) \large\displaystyle\int_{0}^{\frac{\pi}{2}}\ln^{2}(\sin(x))\mathrm dx=\frac{{\pi}^{3}}{a}+\frac{\pi}{b}\ln^{2}{(c)} If the equation above is true for constants a,b,ca,b,c, find a+b+ca+b+c.

This is part of Ordered Disorder.

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