If 3 sin² θ = $2\dfrac{1}{4}$ and θ is less than 90°, find the value of θ.

Given,

$\Rightarrow 3\text{sin}^2 \text{ θ} = \dfrac{9}{4} \\[1em] \Rightarrow \text{sin}^2 \text{ θ} = \dfrac{3}{4} \\[1em] \Rightarrow \text{sin} \text{ θ} = \pm \dfrac{\sqrt{3}}{2}.$

Since, θ is an acute angle.

∴ sin θ = $\dfrac{\sqrt{3}}{2}.$

⇒ sin θ = sin 60°

⇒ θ = 60°.

Hence, θ = 60°.