Morley's triangle

The second Morley triangle is made by rotating line B C toward vertex A about vertex B by angle (B + 2π)/3. It is an equilateral triangle. It has trilinear vertex matrix [1 | 2cos[1/3(C - 2π)] | 2cos[1/3(B - 2π)] 2cos[1/3(C - 2π)] | 1 | 2cos[1/3(A - 2π)] 2cos[1/3(B - 2π)] | 2cos[1/3(A - 2π)] | 1] (Kimberling 1998, p. 165).

first Morley triangle | second Morley adjunct triangle | third Morley triangle