Problem - 3916
Prove $\tan 20^\circ \tan 40^\circ \tan 60^\circ \tan 80^\circ=3$.
Because $\tan 60^\circ = \sqrt{3}$, the given problem is equivalent to show
\begin{equation}
\tan 20^\circ \tan 40^\circ \tan 80^\circ=\sqrt{3}
\end{equation}
This relation indeed hold by the triple tangent formula # 2255 where $\alpha = 20^\circ$.