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\begin{equation}

\phi(u,v)=((r\cos u+a)\cos v, (r\cos u +a)\sin v, r\sin u)

\end{equation}

with \begin{equation}a>0, r\in(0,a)\end{equation}. I want to invert this map to get a chart map for the torus.

Can anyone give me a hand with this?

Thanks!