The value of $$\frac{1}{cosec\theta - cot\theta} - \frac{1}{sin\theta}$$
$$\frac{sin\theta}{1-cos\theta} - \frac{1}{sin\theta}$$
or $$\frac{cos\theta - cos^2\theta}{(1-cos\theta)sin\theta}$$ = $$cot\theta$$
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