The equation of a straight line which passes through the origin and makes an angle α (0 ≤ α ≤ 90°) with the line L: x + √3 y + 3√3 = 0 is x − √3 y = 0. What is the value of α?

Slope of line L: x + √3 y + 3√3 = 0 is m₁ = −1/√3. Slope of line x − √3 y = 0 is m₂ = 1/√3. The angle between them: tan α = |(m₂ − m₁)/(1 + m₁m₂)| = |(1/√3 − (−1/√3))/(1 + (−1/√3)(1/√3))| = |(2/√3)/(1 − 1/3)| = |(2/√3)/(2/3)| = (2/√3)(3/2) = 3/√3 = √3. So α = 60°.