If tan3θ=cot(θ−22
∘
), where 3θ is an acute angle, find the value of θ.

Using the trigonometric identity cotα=tan(90
∘
−α), we can rewrite the given equation:

tan3θ=tan(90
∘
−(θ−22
∘
))
Equating the angles:

3θ=90
∘
−θ+22
∘

3θ+θ=112
∘

4θ=112
∘

θ=
4
112
∘

​
=28
∘