Step 1:
First, we can rewrite the given limit as follows:
$$
\lim _{t \rightarrow 0} \frac{\sin 3 t}{2 t} = \frac{3}{2} \cdot \lim _{t \rightarrow 0} \frac{\sin 3 t}{3 t}
$$
This is because we can factor out the constant $\frac{3}{2}$ from the limit.
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