Problem 3 - Entrance Test

Given √3 tan θ = 1, which implies tan θ = 1/√3. We know that tan 30° = 1/√3. Therefore, θ = 30°. Now, substitute θ = 30° into the expression sin² θ - cos² θ: sin² 30° - cos² 30° = (1/2)² - (√3/2)² = 1/4 - 3/4 = -2/4 = -1/2.