For an integer \( n \geq 4 \), find the solutions of the equation

\[

\sum_{k=1}^n \frac{\sin \frac{k\pi}{n+1}}{\sin (\frac{k\pi}{n+1} -x)} = 0.

\]

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For an integer \( n \geq 4 \), find the solutions of the equation

\[

\sum_{k=1}^n \frac{\sin \frac{k\pi}{n+1}}{\sin (\frac{k\pi}{n+1} -x)} = 0.

\]