1. **Problem statement:** Given $\cot(\theta - 30^\circ) = \frac{1}{\sqrt{3}}$, find $\sin \theta$. 2. **Recall the cotangent values:** $\cot 60^\circ = \frac{1}{\sqrt{3}}$. 3. **Set the angle:** Since $\cot(\theta - 30^\circ) = \cot 60^\circ$, it implies $$\theta - 30^\circ = 60^\circ$$ 4. **Solve for $\theta$:** $$\theta = 60^\circ + 30^\circ = 90^\circ$$ 5. **Find $\sin \theta$:** $$\sin 90^\circ = 1$$ 6. **Answer:** The value of $\sin \theta$ is $1$. Hence, the correct choice is গ) 1.