# De Rham Cohomology: tridimensional space $\mathbb{R}^{3}$ without a circle

I'm a new users. I'd like to calculate the De Rham cohomology of euclidean space $$\mathbb{R}^{3}$$ without a circle $$\mathbb{S}^{1}$$. I don't have idea how to proceed! I saw the answer given to this question here but I don't understand nothing. The only tools that I know are the Mayer-Vietoris sequence and the equivalence of cohomology of homotopic manifolds. I also know the De Rham cohomology of n-dimensional sphere $$\mathbb{S}^{n}$$ and the De Rham cohomology of projective spaces. How can I proceed? Should I use Mayer-Vietoris? Or should I find an homotopy between $$M=\mathbb{R}^{3}$$ \ $$\mathbb{S}^{1}$$ and another manifold simplier to calculate?