The smallest positive angle θ for which cos3θ = −1/2 is:

The smallest positive angle whose cosine is −1/2 is 120°, so the smallest choice is 3θ = 120°, giving θ = 40°. Losing the minus sign leads to 3θ = 60° and the trap 20°; 120° is the value of 3θ, not of θ; and θ = 60° would give cos180° = −1, not −1/2.