In your question, the two great circles have angle between them theta and meet at antipodal points P, P'. To visualise this, take one great circle to be the equator, and imagine the second one as follows: start with a second equator identical in location to the first, and just "tilt" this up the sphere by angle theta. This is then the second great circle. The points P and P' are the points on the equator where we "pivoted" the tilt from.