Question 9
The parabola with equation $y = x^2 - 4$ is rotated $60^\circ$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\frac{a - \sqrt{b}}{c},$ where $a,$ $b,$ and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a + b + c.$