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 \(a+b+c.\)

(第二十四届AIME2 2006 第6题)