10:02 AM
specific-question I am not sure that trigonometric-sums fits here: Sum of $\sin$ when angles shrink by $1/n$
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There are many identities known like $$\sum_{k=0}^{n-1} \sin (k \cdot \theta + \varphi) = \frac{\sin\left(n \cdot \frac{\theta}{2}\right)}{\sin\left(\frac{\theta}{2}\right)} \cdot \sin \left(\frac{2 \varphi + (n-1)\cdot \theta}{2} \right)$$ However, in such situations the angles add up and are eq...
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