If secθ - tanθ = 3, where -90 < θ < 0, then find the value of the expression \(\frac{\text {cosec} \theta - 1}{\text {cosec} \theta + 1}\).

1
\(\frac{1}{9}\)
2
9
3
\(\frac{1}{3}\)
4
More than one of the above
5
None of the above

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