[SOLVED] Complex analysis, determine the set in the complex plane that satisfies...

I've been stuck for 3 days on this simple problem. I must graph the set of the complex plane where z satisfies $\displaystyle |3z+2|<1$. I've used the way of writing $\displaystyle z=re^{i\theta}$ but reached a non sense condition for r. Well, the equation |3z+1|=1 would hold if $\displaystyle r=-\frac{1}{3 \cos \theta} \pm \frac{\sqrt {-2-\sin ^2 \theta}}{3 \cos \theta}$. I really have no idea where I went wrong. I know there's likely an easy way to solve the problem, but still, I don't know where I'm wrong by replacing z for $\displaystyle re^{i\theta}$ and then calculate the modulus of $\displaystyle 3z+2$, etc.