How do I plot in python a cone for which I have the vertex point, line that is the central axis and opening angle?

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I managed to get the equation of a cone for which I have the vertex, opening angle and central axis which the cone must revolve around. A sample is attached below for which they get the equation of a cone given the initial parameters mentioned above. I have tried the meshgrid method where I get the equation in terms of z but there are so many NaNs and I don't get a cone. Does anyone know how to plot the final equation in the image below 1.

Equation of the cone