'gnuplot: Plotting a function on the surface of a sphere

I have a function, say f(theta, phi) = sqrt(1 - (sin(theta)*sin(phi))**2) + 5 * sqrt(1 - (sin(theta)*cos(phi))**2) that I want to plot as a color plot on the surface of a sphere. However, I can't figure out how I have to feed this function into splot in order to achieve this without first generating a file with the appropriate values in a table.

How can I get gnuplot to do this?



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