Trigonometric Equations · Superchallenge problem

The equation $x^3 - 3x - 1 = 0$ has three real roots. They can be written as $2\cos\alpha^\circ$, $2\cos\beta^\circ$, $2\cos\gamma^\circ$ with $0 \le \alpha < \beta < \gamma \le 180$. Find $\alpha + \beta + \gamma$.