If →a and →b are two unit vectors such that →a + →b is also a unit vector, then find the angle between →a and →b.

Let the angle between vectors →a and →b be θ.
Dot product of →a and →b is →a.→b = |→a||→b|cosθ, given that →a and →b are unit vectors. So |→a| = |→b| = 1.
|→a + →b|² = |→a|² + |→b|² + 2|→a||→b|cosθ
Therefore, 1 = 1 + 1 + 2(1)(1)cosθ
1 = 2 + 2cosθ
-1 = 2cosθ
cosθ = -1/2
θ = 2π/3