P10: Given  triangle ABC,  erect  externally  equilateral  triangle P3 on  side AB and  regular hexagon P6 on  side AC. Let D and E be  the  centers  of P3 and P6,  respectively.   Let F be the midpoint of side BC.  Compute ∠DFE.

I got the correct answer by choosing an easy example where ABC is a right triangle, but there is probably a more rigorous way to show that it's 90 degrees for any triangle ABC. Could I maybe get some hints toward how to do that?