Q44 Matemática  (IMO Longlists 1987)

Sejam ${\theta }_1,{\theta }_2,\cdots ,{\theta }_n$ $n$ números reais tais que $\mathrm{sen}{\theta }_1+\mathrm{sen}{\theta }_2+\cdots +\mathrm{sen}{\theta }_n=0$. Prove que $$|\mathrm{sen}{\theta }_1+2\mathrm{sen}{\theta }_2+\cdots +n\mathrm{sen}{\theta }_n|\le \left[\frac{n^2}{4}\right]$$