4. 59 The equation $z^{6}+z^{3}+1=0$ has a complex root, and on the complex plane, the argument $\theta$ of this root lies between $90^{\circ}$ and $180^{\circ}$. Find the degree measure of $\theta$.

The equation $z^{6}+z^{3}+1=0$ has a complex root, and on the complex plane, the argument $\theta$ of this root lies between $90^{\circ}$ and $180^{\circ}$. Find the degree measure of $\theta$.