Prove by means of the function $h: \mathbb{R}^2 \to \mathbb{R}^3$ defined by $h(\theta, \varphi)=((2+ \cos \theta) \cos \varphi, (2+ \cos \theta) \sin \varphi, \sin \theta)$ that $\mathbb{R}^3 \setminus \mathbb{Z}^2$ is difeomorphic to the torus of revolution $\mathbb{T} \subset \mathbb{R}^3$ obtained by rotating around the z axis the circle $C_0$ is in the xz plane, has radius 1 and center $ (2,0,0) $
It is easy to see that a parameter of the torus of revolution is $((2+ \cos \theta) \cos \varphi, (2+ \cos \theta) \sin \varphi, \sin \theta)$, which is the same function $h$. How can I proceed to show the difeomorphism?