Question Number 140338 by Arzoon last updated on 06/May/21
$${if}\:\theta=\frac{\pi}{\mathrm{2}{n}+\mathrm{1}},\:{n}\geqslant\mathrm{1},\:{n}\in{N}\:,{then}\:{prove}\:{that}: \\ $$$${tan}\theta{tan}\mathrm{2}\theta{tan}\mathrm{3}\theta\centerdot\:\centerdot\:\centerdot\:\centerdot\:\centerdot\:\centerdot\:{tan}\left({n}\theta\right)\:=\:\sqrt{\mathrm{2}{n}+\mathrm{1}} \\ $$