Any normal third degree extension of $\mathbb Q$ contained in $\mathbb C$ must be contained in $\mathbb R$

Question

We let $K\subset \mathbb C$ be a finite normal field extension of $\mathbb Q$ such that $[K:\mathbb Q]=3$. Show that $K\subset \mathbb R$.

I know that no cyclotomic extension of $\mathbb Q$ will do the job, as it will have degree $\varphi(n)$ over $\mathbb Q$, which is never $3$. However, how do I prove that this holds for arbitrary normal field extensions?