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Given $$\begin{align*} x&=(2+\cos(2s))\cos(3s)\\ y&=(2+\cos(2s))\sin(3s)\\ z&=\sin(2s),\end{align*}$$ I was wondering how to express these equations as polynomial equations in $x$, $y$, $z$, $a=\cos(s)$, $b=\sin(s)$.

Thanks!

Edit: I expect that the polynomial equations can give the same surface in $\mathbb R^3.$

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