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14
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Accepted
Trigonometric inequality
I will continue from the point where Christophe Leuridan's answer stopped. Denote our sum $S$, then
$$
S=2p\sum_{n=1}^q \frac{\sin(2\pi np/q)}{(1+\cos(2πnp/q))\sin(2\pi n/q)}.
$$
For $n=q$ this is und …