First, be careful with phrasing. Your "the angle between two locations" is unclear. Keeping things to a simple sphere, the azimuth of any great circle route depends entirely on where you measure it. It can range all the way from 0 to 360 and be correct. You probably seek the starting azimuth of a great circle route from a certain point to another point.

Your test points are at strange locations (but it's good to test those situations): they're exactly opposite one another -- they're antipodal points -- and near the poles. The correct azimuth of any oblique great circle route from one point to its antipodal point will always be exactly 90 or 270, depending only on your preference. The general trend of the great circle of your test example is approximately 0 and 180, once you're well away from the poles.

It would be instructive to use an example of New York to London or Moscow, and vice versa, and see any differences.

First, be careful with phrasing. Your "the angle between two locations" is unclear. 

Keeping things to a simple sphere, the azimuth of any oblique great circle route depends entirely on where you measure it. It can range all the way from 0 to 360 and be correct. You probably seek the starting azimuth of a great circle route from a certain point to another point.

Your test points are at strange locations (but it's good to test those situations): they're exactly opposite one another across the globe's diameter -- they're antipodal points -- and they're near the poles. There are always an infinity of possible great circle routes from any one point to its antipodal point!

The azimuth of any oblique great circle route at its most northern and most southern points will always be exactly 90 or 270, depending only on your preferred direction of travel. 

The general trend of the great circle of your test example is approximately 0 and 180, once you're well away from the poles. It would be instructive to use an example of New York to London or Moscow, and vice versa, and see any differences.