If $$cosec \theta + \cot \theta = 2,$$ then $$\sin \theta$$ is:

Given,  $$cosec \theta + \cot \theta = 2$$ ..................(1)

$$=$$>  $$\left(\operatorname{cosec}\theta+\cot\theta\right)\times\frac{\operatorname{cosec}\theta-\cot\theta}{\operatorname{cosec}\theta-\cot\theta}=2$$

$$=$$>  $$\frac{\operatorname{cosec}^2\theta-\cot^2\theta}{\operatorname{cosec}\theta-\cot\theta}=2$$

$$=$$>  $$\frac{1}{\operatorname{cosec}\theta-\cot\theta}=2$$

$$=$$>  $$\operatorname{cosec}\theta-\cot\theta=\frac{1}{2}$$.......................(2)

Adding (1) and (2),

$$\operatorname{cosec}\theta\ +\cot\theta\ +\operatorname{cosec}\theta-\cot\theta=2+\frac{1}{2}$$

$$=$$>  $$2\operatorname{cosec}\theta=\frac{5}{2}$$

$$=$$>  $$\operatorname{cosec}\theta=\frac{5}{4}$$

$$=$$>  $$\sin\theta=\frac{4}{5}$$

Hence, the correct answer is Option A