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The expression of $$\frac{\cot \theta + \cosec \theta - 1}{\cot \theta + \cosec \theta + 1}$$ is equal to
$$\frac{1 + \cos \theta}{\sin \theta}$$
$$\frac{1 - \cos \theta}{\sin \theta}$$
$$\frac{\cot \theta + 1}{\cosec \theta}$$
$$\frac{\cot \theta - 1}{\cosec \theta}$$
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