The isosceles right triangle ABC has its right angle at B and has area 1. The rays trisecting \(\angle ABC\) intersect AC at E and F, where E is closer to A than it is to C. The area of \(\triangle BEF\) can be written in the form \(a-b\sqrt{c}\) for positive integers a, b, and c such that c square-free. Determine a+b+c.
