When 0° < θ < 90°, solve the following equation:

tan² θ = 3 (sec θ - 1).

Given,

tan² θ = 3 (sec θ - 1)

On Solving,

⇒ sec² θ - 1 = 3 sec θ - 3

⇒ sec² θ - 1 - 3 sec θ + 3 = 0

⇒ sec² θ - 3 sec θ + 2 = 0

⇒ sec² θ - 2 sec θ - sec θ + 2 = 0

⇒ sec θ (sec θ - 2) - 1(sec θ - 2) = 0

⇒ (sec θ - 1)(sec θ - 2) = 0

⇒ sec θ - 1 = 0 or sec θ - 2 = 0

⇒ sec θ = 1 or sec θ = 2.

If, sec θ = 1
sec θ = sec 0°
θ = 0°.

Given, θ > 0° hence, θ = 0° is not possible.

∴ sec θ = 2

⇒ sec θ = sec 60°

⇒ θ = 60°.

Hence, the value of θ = 60°.