Logarithms, Trigonometry, Integrals, Part 2

Calculus Level 5

0π/2ln(sinx)ln(tanx) dx \displaystyle \int _{0}^{\pi/2} \ln(\sin x) \ln(\tan x) \space \mathrm{d}x

Given that the above integral equals to πAB \frac {\pi^A}{B} for positive integers A,BA,B, what is the value of A+BA+B?

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