help roots of unity question

If $re^{i \theta}$ is a root of $z^8 - z^7 + z^6 - z^5 + z^4 - z^3 + z^2 - z + 1 = 0$, where $r > 0$ and $0 \le \theta < 2 \pi,$ then find the sum of all possible values of $\theta.$