Q14 Matemática  (IMO Longlists 1970)

Seja $\alpha +\beta +\gamma =\pi$. Prove que ${\sum }_{cyc}\mathrm{sen}2\alpha =2\cdot \left({\sum }_{cyc}\mathrm{sen}\alpha \right)\cdot \left({\sum }_{cyc}\cos alpha\right)-2{\sum }_{cyc}\mathrm{sen}\alpha$.