2014 AIME II Problem 11

In \triangle RED, \measuredangle DRE=75^{\circ} and \measuredangle RED=45^{\circ}. |RD|=1. Let M be the midpoint of segment \overline{RD}. Point C lies on side \overline{ED} such that \overline{RC}\perp\overline{EM}. Extend segment \overline{DE} through E to point A such that CA=AR. Then AE=\frac{a-\sqrt{b}}{c}, where a and c are relatively prime positive integers, and b is a positive integer. Find a+b+c.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.