Given a sphere with center at the origin, the great circle through two points P1 and P2 on...

Given a sphere with center at the origin, the great circle through two points P1 and P2 on the sphere is the circle with center at the origin that passes through P1 and P2. The great circle distance between P1 and P2 is the length of the arc on the great circle. Find the great circle distance between the following pairs of points (given in spherical coordinates):

(a) (3, π/4, π/6), (3, π/4, 3π/4)

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(b) (2, π/3, π/2), (2, 7π/6, π/2)

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(c) (1, π/4, 0), (1, π/2, π/4)