C.a.R. > Applications > Difficult > Morley Tirangle
This is proof due to D.J.Newman I found in the web.
The idea to start with a equilateral triangle and arbitrary angles α+β+γ=60. Then construct A, B and C. We have to show φ=α finally. To do this, use the sine theorem.
There is not much space for the angles here. So we use invisible angles. The labels are shown nevertheless.