How can you compute the sum of the angles on a non-euclidean surface, on the surface of a $S^2$ sphere for example ?
I know that (for an elliptic geometry) if the triangle is small enough, the sum would be $180$ degrees, and grow with the size of the triangle, so there might be an integral over the triangle involved, and the metric tensor would be of some use at one point...
So if you could give the outline and directions, it will be a good start to know which notions to check and learn, even if I do not understand the answer immediately.
Thank you for your help,
JD