# Paneer Definite Masala 9

Calculus Level 5

$\large \int_0^{\pi /4} \arctan \left( \dfrac{2\cos^2 \theta}{2-\sin2\theta} \right) \sec^2 \theta \, d\theta$

If the integral above can be expressed as $$\dfrac{A\pi^B}C - D \ln E$$, where $$A,B,C,D$$ and $$E$$ are positive integers, with $$A$$ and $$B$$ being coprime integers, find $$A+B+C+D+E$$.

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