The angle between the true great-circle track and the true rhumb-line track is conversion angle which is half convergency.
Convergency = Change of Longitude x sine mean Latitude
Change of Longitude = 360º - (165ºW + 177ºE) = 360º - 342º = 18º
Mean Latitude is 60ºS and sin60º = 0.866
Conversion angle = ½ x 18º x 0.866 = 7.8º.