If tan4θ = cot(θ + 20°), find the value of θ if 4θ is an acute angle. - Mathematics

If tan4θ = cot(θ + 20°), find the value of θ if 4θ is an acute angle.

Sum

tan4θ = cot(θ + 20°)
⇒ cot(90° - 4θ) = cot(θ + 20°)
⇒ 90° - 4θ= θ+ 20°
⇒ 5θ = 70°
⇒ θ = 14°.

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