Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function defined by
$$
f(x)=\left\{\begin{array}{cc}
x^2 \sin \left(\frac{\pi}{x^2}\right), & \text { if } x \neq 0 \\
0, & \text { if } x=0 .
\end{array}\right.
$$
Then which of the following statements is TRUE?
Select the correct option:
A
$f(x)=0$ has infinitely many solutions in the interval $\left[\frac{1}{10^{10}}, \infty\right)$.
B
$f(x)=0$ has no solutions in the interval $\left[\frac{1}{\pi}, \infty\right)$.
C
The set of solutions of $f(x)=0$ in the interval $\left(0, \frac{1}{10^{10}}\right)$ is finite.
D
$f(x)=0$ has more than 25 solutions in the interval $\left(\frac{1}{\pi^2}, \frac{1}{\pi}\right)$.
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