If you had your longitude/latitude, and the time/date, how could I go about working out the angle between your normal and the sun?

At first I was doing a simplistic approach of assuming elliptical orbit in only two dimensions and that the earth is a perfect sphere,

Can I get a more accurate method /formula than this that can be evaluated in one step without any iterative methods?

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Here is rough example of what I mean, say the green plane is the point on the surface of the earth I want.

The angle I seek is between the black line perpendicular to the green plane and the black line between the plane and the sun.

There are 2 problems involved here, knowing how the normal changes as the non spherical earth rotates and knowing the relative position between the earth and the sun. Any help appreciated.


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