The total torsion of a unit speed curve γ : [a, b] → R3 is defined to be. ∫ τ(s) ds (bounds a to b), where τ(s) is the torsion of γ at the point γ(s). If γ is a closed curve on the unit sphere S2, show that γ has zero total torsion. I have a couple hints to solve this but I can't figure it out, the hints are use k(T)=K_γ cos θ where T=γ' for a unit speed curve γ, and differentiate cosθ=N · U