Given: \[ \csc \theta + \cot \theta = \sqrt{3} \quad \text{-----(i)} \] Also, \[ \because \csc^2 \theta - \cot^2 \theta = 1 \] \[ \Rightarrow (\csc \theta + \cot \theta)(\csc \theta - \cot \theta) = 1 \] \[ \Rightarrow \sqrt{3}(\csc \theta - \cot \theta) = 1 \] \[ \Rightarrow \csc \theta - \cot \theta = \frac{1}{\sqrt{3}} \quad \text{-----(ii)} \] Adding equations (i) and (ii): \[ 2 \csc \theta = \sqrt{3} + \frac{1}{\sqrt{3}} \] \[ \Rightarrow 2 \csc \theta = \frac{3 + 1}{\sqrt{3}} = \frac{4}{\sqrt{3}} \] \[ \Rightarrow \csc \theta = \frac{2}{\sqrt{3}} \] \[ \Rightarrow \sin \theta = \frac{\sqrt{3}}{2} \]