I agree, in general, with the comments of peace*out and Bonanova, but I think you are still dealing with finite sheres. Once you expand the sphere to the infinite a regular triangle inscribed on the surface is bound to be regular. And peace*out, at the infinite would not the depth cease to exist?
There are two coins in an opaque bag. They are identical except one is a heads and a tail; the other has two heads. What are your odds of getting two heads if you withdraw one coin at random, place it face down on the desk, and continue by doing the same with the second coin?