Three 60 degree sectors of a unit circle pack neatly inside an equilateral triangle. The side length of this triangle can be written as $\displaystyle A+\frac{B}{\sqrt{C}}$, where $\displaystyle A, B, C$ are integers with $\displaystyle C$ square-free. What is the value of $\displaystyle A+B+C$? Anyone please help me.