In \triangle R E D, R D=1, \angle D R E=75^{\circ} and \angle R E D=45^{\circ}. Let M be the midpoint of segment \overline{R D}. Point C lies on side \overline{E D} such that \overline{R C} \perp \overline{E M}. Extend segment \overline{D E} through E to point A such that C A=A R. Then A E=\frac{a-\sqrt{b}}{c}, where a and c are relatively prime positive integers, and b is a positive integer. Find a+b+c.