Although I have a background in mathematics, I confess to having never heard of ‘Morley’s Miracle’ until a few years ago when it was brought to my attention by a friend, a former high school mathematics teacher. The ‘miracle’ is a theorem in elementary geometry stating that the trisectors of the angles of a triangle intersect in three points that form the vertices of an equilateral triangle. There are many solutions posted on the internet. The one I came up with involves only elementary trigonometry and the Law of Sines. It is perhaps slightly simpler than, although very similar to the first proof given here which uses both the Law of Sines and the Law of Cosines.
Click on this link to see my solution.