If 2cosec²θ + 3cot²θ = 17, then find the value of θ for 0° ≤ θ ≤ 90°.

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Given: 2cosec²θ + 3cot²θ = 17

Recall that:
cosec²θ = 1 + cot²θ

Let x = cot²θ
So, cosec²θ = 1 + x

Substitute into the equation:
2(1 + x) + 3x = 17
2 + 2x + 3x = 17
2 + 5x = 17
5x = 15
x = 3

So, cot²θ = 3
cotθ = √3 (since 0° ≤ θ ≤ 90°, cotθ is positive)

cotθ = √3 ⇒ θ = 30°

Therefore, the value of θ is 30°.

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