Complex integral and parametrization of a circle

Question

I am trying to compute the following integral of $$\int \frac{1}{z^3+3} dz$$ over a circle of radius $2$, centerd at $(2,0)$. Thus I am trying to compute the residue and have found that the function has poles at $$3^{\frac{1}{3}}\left[ \frac{\sqrt{3}-i}{2} \right], \; i3^{\frac{1}{3}}, \text{ and } -3^{\frac{1}{3}} \left[ \frac{\sqrt{3}+i}{2} \right].$$ However, we have to make sure that all the roots lie inside our parameter. My conjecture is they all lie inside our given parameter. Thus, is there any "formal" way to prove that those poles lie inside the given circle?