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Feb 4, 2014 at 18:49 comment added Anton Petrunin If one of the angles is smaller than $\pi$ then you can make shortcut in the angle.
Feb 4, 2014 at 18:26 comment added Poincare-Lelong Yes, I should have said $\alpha,\beta < 1$. Could you please elaborate on your answer? Why does the geodesic cut the cone into two angles with measure greater than $\pi$?
Feb 1, 2014 at 5:33 history answered Anton Petrunin CC BY-SA 3.0