An integral to lean on!

Calculus Level 5

Let \(\large \displaystyle A = \int_{\pi /5}^{\pi /4} \cot ^{3} x \ln \sin x dx\)

\(\large \displaystyle B = \int_{\pi /5}^{\pi /4} \dfrac{\csc ^{2} x}{\tan x} \ln ^{2} \sin x dx\)

Let \(C = A-B\)

Find \(\lfloor -10000C \rfloor\).

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