Logarithms, Trigonometry, Integrals, Part 2

Calculus Level 5

\[ \displaystyle \int _{0}^{\pi/2} \ln(\sin x) \ln(\tan x) \space \mathrm{d}x \]

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

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