Whyto you want get rid of ? That is supposed to be one of the parameters. The point of using and as parameters instead of, say, and , is that is constant here. I wonder if you weren't mistakenly thinking you were supposed to have and as parameters?

If we set y= 0 so we are looking at the x,z-plane, the equation becomes and, since that has a constant slope, so . Then and . Put those into the equations for x, y, and z in spherical coordinates.