Suppose that triangle ABC is an acute-angle triangle, D is the foot of the altitude from A and D1 and D2 are the reflections of D with respect to AB and AC, respectively. Let F and E be the feet of the altitudes from C and B respectively. Show that the points F, E, D1, D2 are collinear.

I am thinking that if I can show that angle = angle = angle then that would show the points are collinear. I had a thought I can establish this using cyclic quadrilaterals but I got stuck. I can use some help on what to do next.

Thanks.