\(A, B\) and \(C\) are three points on a plane such that \(AB = BC =1\) and \(CA = \sqrt{3}\) Draw three circles whose diameters are \(\overline{AB}, \overline{BC}\) and \(\overline{CA}\) respectively. The area of the region included in all three circles (the grey region below) is \(\frac{a}{b} \pi + \frac{\sqrt{c}}{d}\) 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.

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ItsFree Feb 24, 2023