If 3θ is an acute angle, solve the following equations for θ :

(i) 2 sin 3θ = $\sqrt{3}$

(ii) tan 3θ = 1.

(i) Given,

⇒ 2 sin 3θ = $\sqrt{3}$

⇒ sin 3θ = $\dfrac{\sqrt{3}}{2}$

⇒ sin 3θ = sin 60°

⇒ 3θ = 60°

⇒ θ = $\dfrac{60\degree}{3}$

⇒ θ = 20°.

Hence, θ = 20°.

(ii) Given,

⇒ tan 3θ = 1

⇒ tan 3θ = tan 45°

⇒ 3θ = 45°

⇒ θ = $\dfrac{45\degree}{3}$

⇒ θ = 15°.

Hence, θ = 15°.