I need to represent the cone $z=\sqrt{3x^2+3y^2}$ parametrically in terms of $\rho$ and $\theta$ where $(\rho,\theta,\phi)$ are spherical coordinates.
Attempt. I tried using: $x=\rho\sin\phi\cos\theta \\y=\rho\sin\phi\sin\theta\\z=\rho\cos\phi$
and $\rho^2=x^2+y^2+z^2\\\cos\phi=\frac{z}{\sqrt{x^2+y^2+z^2}}\\\rho^2\sin^2\phi=x^2+y^2$
I cannot find a way to get rid of $\phi$. Hints please.
This is the graph of it. It is a cone.