Let A and B be points on circle \Gamma such that A B=\sqrt{10}. Point C is outside \Gamma such that \triangle A B C is equilateral. Let D be a point on \Gamma and suppose the line through C and D intersects A B and \Gamma again at points E and F \neq D. It is given that points C, D, E, F are collinear in that order and that C D=D E=E F. What is the area of \Gamma?