If the two longitudes add up to 180° and they are in opposite
hemispheres (East and West) then they are directly opposite each other, and
provided the two positions are also in the same Northern (or Southern)
Hemisphere then the shortest route between the two points will be over the
relevant Pole.
Add the two latitudes together.
Subtract the sum from 180°.
Multiply the answer by 60'.
The product is a number in Minutes of Arc which, along a Meridian (any Great
Circle Track through the Pole is a Meridian) is equal to the distance in NM.