In the given figure , \(\Delta ABC\) is an equilateral triangle with side as 1 unit.

The given circle is the in-circle of \(\Delta ABC\)

If Area of red colored region can be expressed as:

\[\dfrac{a\sqrt{b} - c}{d}\] where \(a,b,c,d\in \mathbb{N}\) ,\(b\) is independent of a perfect square ,

Find \(a + b + c + d\)

**Details and Assumptions**:-

- Take \(\pi\) as \(\dfrac{22}{7}\).

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