+566 A, B, and C are three points on a plane such that AB=BC=1 and CA= sqrt 3. Draw three circles whose diameters are AB},BC, and CA, respectively. The area of the region included in all three circles (the grey region below) is \(\dfrac a b \pi +\dfrac {\sqrt c} d\) in simplest form, so a, b, c, d are positive integers, a and b are relatively prime, and c is not divisible by the square of a prime. Enter the values of a,b,c,d in order, separating by commas.
