There are many ways to derive the Equation of Time, depending on one’s need for accuracy.
The easiest is the Fourier Method which gives acceptable accuracy for most gnomonic work.
If you want more thorough Astronomical calculations that provide exceptional accuracy and much more information about the position of the sun, then Kepler's Method is preferred.
If you want the ultimate accuracy, it is best to use NASA/JPL's Method
All three methods are described below with links to Excel Spreadsheets for the Fourier and Kepler methods.
