Let C be the circle of radius 1 with center (2, 0) in the xz-plane, considered as a subset of R³ in xyz coordinates. The torus is the subset of R³ obtained by rotating C once around the z-axis. From here, the torus will also be denoted T². Please answer the following question of T², which you may assume is a smooth surface.
Select two charts which intersect, and compute the transition function from one to the other.