Keep calm and Integrate

Calculus Level 4

π/4π/312csc(2x)[ln(sin2(x))ln(cos2(x))]2dx\int_{\pi/4}^{\pi/3}12\csc (2x)[\ln(\sin^2(x))-\ln(\cos^2(x))]^2 \, dx

If the above integral equals (lnb)a(\ln b)^a, where aa and bb are positive integers, find a+ba+b.

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