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We are given that,

tan^-1 (cot θ) = 2θ

We need to find the value of θ.

We have,

tan^-1 (cot θ) = 2θ

Taking tangent on both sides,

⇒ tan [tan^-1 (cot θ)] = tan 2θ

Using property of inverse trigonometry,

tan(tan^-1 A) = A

⇒ cot θ = tan 2θ

Or,

⇒ tan 2θ = cot θ

Using the trigonometric identity,

Using the trigonometric identity,

By cross-multiplying,

⇒ tan θ × 2 tan θ = 1 – tan² θ

⇒ 2 tan² θ = 1 – tan² θ

⇒ 2 tan² θ + tan² θ = 1

⇒ 3 tan² θ = 1

And .

Thus,