halfway of this great circle track, we find a rhumb line heading, if I were to use this heading I found halfway of the great circle, and take off and maintain such heading at the departure airport.
The rhumb line track that takes you to the destination airport will be somewhere between the start track for the great circle and the end track for the great circle. It's only the track at the midpoint in special cases (e.g. dep and dest on the same parallel).