If tan θ = cot θ and 0° ≤ θ ≤ 90°, state the value of θ.

tan θ = cot θ

$\dfrac{\text{sin θ}}{\text{cos θ}} = \dfrac{\text{cos θ}}{\text{sin θ}}$

$\text{sin}^2 \text{θ} = \text{cos}^2 \text{θ}$

As we know that sin² θ + cos² θ = 1

⇒ sin² θ + sin² θ = 1

⇒ 2sin² θ = 1

⇒ sin² θ = $\dfrac{1}{2}$

⇒ sin θ = $\dfrac{1}{\sqrt2}$

⇒ sin θ = sin 45°

⇒ θ = 45°

Hence, the value of θ = 45°.