\frac{2}{\pi}\int_{0}^{\pi/2} \frac{ \cos^{2}x}{\sin^{2}x+4\cos^{2}x} dx\frac{2}{\pi}\int_{0}^{\pi/2} \frac{ \cos^{2}x}{\sin^{2}x+4\cos^{2}x} dx

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