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 \(\theta.\)