Third Method in Proving $\tan^2 20^{\circ}+\tan^2 40^{\circ}+\tan^2 80^{\circ}=33$

As a good mathematics educator, we should solve the best quality math problems using as many ways as we could, because each solution has its own learning value. Who knows, students might gain something from the long and tedious method of problem solving method and one day, they will surprise us with the improved version of the solution!

One thing every mathematics educator has to remember is that our imaginations are vibrant, our hearts are open, everything about math amazes us, and we think anything is possible.