An odd sign

Geometry Level pending

Find

$\sin\frac{\pi}{n} + \sin\frac{3\pi}{n} + \sin\frac{5\pi}{n} +\ldots+\sin\frac{n\pi}{n}$

$$Hint:2\sin { A } \sin { B } =\quad \cos { (A-B) } -\cos { (A+B) }$$

(This question was given by our teacher.)

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