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

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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