Evaluate the following limits: \[ \lim _{x \rightarrow 0} \frac{\sin ^{2} 4 x^{2}}{x^{4}} \]

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Evaluate the following limits:
\[
\lim _{x \rightarrow 0} \frac{\sin ^{2} 4 x^{2}}{x^{4}}
\]
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