In quadrilateral A B C D, A B=2, A D=3, B C=C D=\sqrt{7}, and \angle D A B=60^{\circ}. Semicircles \gamma_{1} and \gamma_{2} are erected on the exterior of the quadrilateral with diameters \overline{A B} and \overline{A D}; points E \neq B and F \neq D are selected on \gamma_{1} and \gamma_{2} respectively such that \triangle C E F is equilateral. What is the area of \triangle C E F?