Question Number 100581 by Dwaipayan Shikari last updated on 27/Jun/20
$${If}\:\alpha=\frac{\mathrm{2}\pi}{\mathrm{7}} \\ $$$${then}\:{prove}\:{that} \\ $$$${tan}\alpha{tan}\mathrm{2}\alpha+{tan}\mathrm{2}\alpha{tan}\mathrm{4}\alpha+{tan}\mathrm{4}\alpha{tan}\alpha=−\mathrm{7} \\ $$