A complex equation

Algebra Level 5

z6+z3+1=0\large z^6 + z^3 +1 =0

If reiθr{e^{i\theta}} is a root of above equation with 90<θ<18090^\circ < \theta < 180^\circ and r>0r > 0, what is the possible value of θ\theta in degrees?

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