2006 AIME II Problem 6

Square ABCD has sides of length 1. Points E and F are on \overline{BC} and \overline{CD}, respectively, so that \triangle AEF is equilateral. A square with vertex B has sides that are parallel to those of ABCD and a vertex on \overline{AE}. The length of a side of this smaller square is \frac{a-\sqrt{b}}{c}, where a, b, and c are positive integers and b is not divisible by the square of any prime. 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.