Geometry Problem Problem 546: Triangle, Angle Trisectors, 60 Degrees, Equilateral triangle

The figure shows a triangle ABC with AD and AE trisectors of angle BAC (angles BAD=DAE=EAC=a), and CE and CF trisectors of angle ACB (angles ACE=ECF=FCB=c). If angle AED=60+c, and angle CEF=60+a, prove that the triangle DEF is an equilateral triangle.