If a sphere is rotated so that point $90°$N $0°$E is moved along a great circle to point $50°$N $6°$E, to which point is point $18°$N $77°$E moved?
$90°$N $0°$E $\implies 50°$N $6°$E
$18°$N $77°$E $\implies ?$
Is there a general formula involving spherical coordinates?