Integration

Calculus Level 4

\[ \large \int_{0}^{{\pi} / {4}} \frac{\sin^2(5\theta)}{\sin^2(\theta)} - \frac{\cos^2(5\theta)}{\cos^2(\theta)} \, d\theta \]

If the integral above can be expressed as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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