Problem 190. Great Circle Distance

I agree. Polar angles are, by convention, measured from the pole, but in this problem you have to consider them to be measure from the equator if you wish to agree with the test cases.

I think considering polar angles measured from pole or from equator does not affect the result in this problem. But if you consider polar angle of the first point measured from pole and the polar angle of the second one from equator it will produce misleading solutions. So, you need to stabilish the same convention for both points.

The problem here is azimuth and polar angle aren't well-defined in the mathematics world. Azimuth would typically be given as the angle from North, and none of the angles given are that.
For people doing this problem for the first time, you should consider the given angles to be latitude and longitude.