It Seems Just Like (corrected)

Calculus Level pending

\[\displaystyle \int_{0}^{\pi/4}\dfrac{4\sin^{4}(x)+\sin^{2}(2x)}{4-4\sin^{2}(x)} \mathrm{d}x\]

If the value of the integral above can be expressed as \(A-\dfrac{\pi}{B}\) for positive integers \(A,B\), find the value of \(A+B\).

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