Step 1: Understanding the Concept:
The property $\sin^{-1}(\sin \theta) = \theta$ only holds true if $\theta$ is in the principal value branch of $\sin^{-1}$, which is $[-\pi/2, \pi/2]$.
Step 2: Formula Application:
Here, $\theta = \dfrac{3\pi}{5}$. Since $\dfrac{3\pi}{5}>\dfrac{\pi}{2}$ (as $0.6\pi>0.5\pi$), it lies outside the principal range. We must use the identity $\sin(\pi - x) = \sin x$.
Step 3: Explanation:
$$\sin \left( \dfrac{3\pi}{5} \right) = \sin \left( \pi - \dfrac{3\pi}{5} \right) = \sin \left( \dfrac{2\pi}{5} \right)$$
Now, $\dfrac{2\pi}{5}$ (which is $0.4\pi$) falls within the range $[-\pi/2, \pi/2]$.
Therefore, $\sin^{-1} \left( \sin \dfrac{2\pi}{5} \right) = \dfrac{2\pi}{5}$.
Step 4: Final Answer:
The correct value is $2\pi/5$.