Morley Equilateral Triangles

Terry Tam
For triangle ABC, the intersections of interior angle trisectors form an equilateral triangle DEF. Intersections of exterior angle trisectors form another equilateral triangle PQR. Together with the intersections of interior and exterior angle trisectors, 3 more equilateral triangles PLM, QJK, RNO are formed. Also, LPQK, MPRO and NRQJ are 3 straight lines.