\[\large I_{n}=\int^{\pi}_{0}\dfrac{\sin \left\{ \left(n+\frac{1}{2}\right)x\right\} }{\sin \frac{x}{2} } dx, \quad n\in \mathbb{W}\]

Find the value of \(\displaystyle \frac{1}{\pi}\sum^{100}_{n=1}I_{n}\).

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