Trigonometry · Superchallenge problem

Two cities both lie at latitude $60^\circ$ N, on opposite sides of the Earth (their longitudes differ by $180^\circ$). Treat the Earth as a sphere of radius $3960$ miles. A plane can fly from one city to the other due east along the $60^\circ$ N parallel, or along the meridians straight over the North Pole. How many miles shorter is the route over the pole? Give the exact value.