Given $\alpha\in \Bbb C$ trascendental , and such that $|\alpha|=1$ (I don't know if this is necesary but I need only this case). Then I have to prove that the polynomial $x^3-\alpha \in \Bbb Q(\alpha)[x]$ is irreducible.
I want to prove this because this is a way to prove that the angle given by $\alpha$ cannot be trisected with rule and compass.