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IMO Shortlist 1969 problem 38

1969 shortlist
(HUN 5) Let r and m (r \le m) be natural numbers and Ak =\frac{2k-1}{2m}\pi. Evaluate \frac{1}{m^2}\displaystyle\sum_{k=1}^{m}\displaystyle\sum_{l=1}^{m}\sin(rA_k)\sin(rA_l)\cos(rA_k-rA_l)

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1969 shortlist
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1969 shortlist
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