If sec2θ = cosec3θ, find the value of θ if it is known that both 2θ and 3θ are acute angles. - Mathematics

If sec2θ = cosec3θ, find the value of θ if it is known that both 2θ and 3θ are acute angles.

Sum

sec2θ = cosec3θ
⇒ sec2θ = sec(90° - 3θ)
⇒ 2θ = 90° - 3θ
⇒ 5θ = 90°
⇒ θ = 18°.

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