As the title says, given that $\theta^3 + 11\theta - 4 = 0$, I'm trying to prove that $\frac{-\theta + \theta^2}{2}$ is an algebraic integer in $K = \mathbb{Q}(\theta)$.

I know that $x^3 + 11x -4$ is irreducible in $\mathbb{Q}[x]$ since it's irreducible in $\mathbb{F}\_3[x]$. I also know that the set of algebraic integers forms an integral domain and thus I know that $-\theta + \theta^2$ is an algebraic integer, unfortunately that's the best I can do with that method since $\frac{1}{2}$ is specifically not an algebraic integer. 

Clearly I need to somehow use the polynomial to solve this, but I can't see how, can anyone point me in the right direction? Thanks.