Yay

2sin⁻¹(sqrt(2+(1−P)cos(φ₁+φ₂)−(1+P)cos(φ₁−φ₂))/2)

where P=cos(θ₁−θ₂).

Phew.

Edit:

cos⁻¹(cosφ_Dcos²θ_A−cosφ_Ssin²θ_A)

where φ_S=φ₁+φ₂, φ_D=φ₁−φ₂ and θ_A=(θ₂−θ₁)/2.