Express some equations as polynomial equations 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 $\mathbb R^3.$

$$\begin{align*}
x^2&=(2+\cos(2s)^2\cos(3s)^2\\
y^2&=(2+\cos(2s)^2\sin(3s)^2\\

x^2+y^2&=(2+\cos(2s))^2(\cos(3s)^2+sin(3s)^2)=(2+\cos(2s))^2\\

x^2+y^2&=(2+\cos(2s))^2=4+4\cos(2s)+\cos(2s)^2=4+4\cos(2s)+(1-\sin(2s)^2)\\

x^2+y^2&=5+4\cos(2s)-z^2\\

x^2+y^2+z^2&=5+4(\cos(s)^2-\sin(s)^2)\\

x^2+y^2+z^2&=5+4a^2-4b^2\\







,\end{align*}$$
$$x^2+y^2+z^2-4a^2+4b^2-5=0$$
