ABC is a triangle with area equal to 20 . The incircle of triangle ABC has radius equal to 2 and the circumcircle of triangle ABC has radius equal to 6 . If sinA+sinB+sinC=a/b , where a and b are coprime positive integers, what is the value of a+b ?

Question

ABC  is a triangle with area equal to 20 . The incircle of triangle ABC  has radius equal to 2  and the circumcircle of triangle ABC  has radius equal to 6 . If sinA+sinB+sinC=a/b   , where a  and b  are coprime positive integers, what is the value of a+b ?