Care to reduce?

2sin^{−1}(sqrt((1−cos*φ*_{1}cos*φ*_{2}cos(*θ*_{1}−*θ*_{2})−sin*φ*_{1}sin*φ*_{2})/2))

Reducing this would work too. _-_ (*P*=cos(*θ*_{1}−*θ*_{2}))

2sin^{−1}(sqrt((1−*P*cos*φ*_{1}cos*φ*_{2}−sin*φ*_{1}sin*φ*_{2})/2))

By the way, the formula above is the angle ∠*AOB* where *A* and *B* are two points with spherical coordinates (*ρ*,(*π*/2)−*φ*_{1},*θ*_{1}) and (*ρ*,(*π*/2)−*φ*_{2},*θ*_{2}), *ρ*≠0, and *O* is the origin. ((*π*/2)−*φ* means that *φ* is the latitude, not the azimuth.)