[math-fun] Solid angle of a spherical triangle

I came across an interesting formula in an optics book for the solid angle of a spherical triangle.  Let a, b, c, be the unit vectors from the center to the vertices of a spherical triangle on the unit sphere.  Then the solid angle Omega, which equals the area of the triangle, is given by tan(Omega/2) = [a,b,c] / (1 + b.c + a.c + a.b), where a.b etc. are dot products, and [a,b,c] is the scalar triple product.  This paper is the cited reference. http://www.maa.org/sites/default/files/Eriksson14108673.pdf   --  Gene