The preceding algorithms are troubled by the singular problem of some formulas and the azimuth multi-value problem in the solution of trigonometric equations. In this paper, sine cosine theorem for spherical triangle is applied in the Mathematica computer algebra system to address and resolve the geodetic problem at special positions such as equator, meridian circle, south and north poles. The algorithm is optimized to avoid tedious quadrant determination. On this basis, a formally simple method for solution is proposed to be applicable under all circumstances, and greatly improve the accuracy of solution. As revealed by data verification, the improved algorithm is greatly efficient in computation, symbolically simpler, and highly universal, proving its significance to the guarantee for surveying and mapping.
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