If tan 3 θ = cot(θ - 22°), where 3 θ is an angle, find the value of θ.
28°
The correct answer is 28°.
In problems involving angles like this, where a condition like "$3\theta$ is an acute angle" is given, it helps restrict the possible values of $\theta$. Complementary angle identities are very useful when an equation involves different trigonometric functions (like tan and cot, or sin and cos) on opposite sides. Always verify your final answer by substituting it back into the original equation and checking if any given conditions (like an angle being acute) are met.
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