dps
posted by manpreet .
If a and b are two unit vectors and θ is the angle between them, then a+b is a unit vector if θ is

without loss of generality, we can let
a = <1,0>
b = <cosθ,sinθ>
a+b = <(1+cosθ),sinθ>
a+b^2 = (1+cosθ)^2 + sin^2 θ
if a+b is a unit vector,
a+b^2 = 1
1+2cosθ+cos^2θ + sin^2θ = 1
1+2cosθ = 0
cosθ = 1/2
θ = 2pi/3