Parametric representation of rectangular form in terms of parameters $\rho$ & $\theta$ 
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.


If you have $z=\sqrt{3x^2+3y^2}$ and $z^2=3x^2+3y^2$, making the appropriate replacements in $\cos\phi=\dfrac{z}{\sqrt{x^2+y^2+z^2}}$ gives
$$\cos\phi=\dfrac{z}{\sqrt{\frac{z^2}{3}+z^2}}$$
Can you see what to do next? (Hint: your Cartesian equation guarantees that $z$ is always positive, so $\sqrt{z^2}=?$)
