For a positive integer \( n \), let \( I_{n}=\int_{-\pi}^{\pi}\left(\frac{\pi}{2}-|x|\right) \co...

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For a positive integer \( n \), let \( I_{n}=\int_{-\pi}^{\pi}\left(\frac{\pi}{2}-|x|\right) \cos n x d x \)
Find the value of \( \left[I_{1}+I_{2}+I_{3}+I_{4}\right] \) where [.] denotes greatest integer function.
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