If θ is a positive acute angle and 4cos²θ - 1 = 0, then the value of tan(θ - 30°) is equal to?

Question: If θ is a positive acute angle and 4cos²θ - 1 = 0, then the value of tan(θ - 30°) is equal to?

Solution:
Given,
4cos²θ - 1 = 0
⇒ 4cos²θ = 1
⇒ cos²θ = 1/4
⇒ cosθ = 1/2
⇒ cosθ = cos60°
∴ θ = 60°

Now,
tan(θ - 30°) = tan(60° - 30°)
= tan 30°
= 1/√3