Can the Law of Sines in Spherical Trigonometry be derived from Gauss Bonnet Theorem?
EDIT1:
To express what went through my mind so far: Started with 3 geodesic circle arcs ... angles at corners can be identified in GB Thm, Area is linkable to solid angle in steridians, but main stumbling block is how to rope in angle subtended at sphere center? GB theorem afaik is a strongly isometric statement born and made entirely from the first fundamental form, but trying to "somehow" incorporate second fundamental form for tangential rotations is what beats me.