In regular pentagon A B C D E, let O \in C E be the center of circle \Gamma tangent to D A and D E. \Gamma meets D E at X and D A at Y. Let the altitude from B meet C D at P; if C P=1, the area of \triangle C O Y can be written in the form \frac{a}{b} \frac{\sin c^{\circ}}{\cos ^{2} c^{\circ}}, where a and b are relatively prime positive integers and c is an integer in the range (0,90). Find a+b+c.