Start with the left-hand side:

\(\frac{\tan \theta}{\sin \theta} - \frac{\sin \theta}{\tan \theta}\)

Substitute \(\tan \theta = \frac{\sin \theta}{\cos \theta}\):

\(\frac{\frac{\sin \theta}{\cos \theta}}{\sin \theta} - \frac{\sin \theta}{\frac{\sin \theta}{\cos \theta}}\)

Simplify each term:

\(\frac{1}{\cos \theta} - \sin \theta \cos \theta\)

Combine the terms over a common denominator:

\(\frac{1 - \cos^2 \theta}{\cos \theta}\)

Use the identity \(1 - \cos^2 \theta = \sin^2 \theta\):

\(\frac{\sin^2 \theta}{\cos \theta}\)

Recognize this as \(\tan \theta \sin \theta\):

\(\tan \theta \sin \theta\)