Let the function \( f : \mathbb{R} \to \mathbb{R} \) be defined by
\( f(x) = \frac{\sin x}{e^{\pi x}} \left( \frac{x^{2023} + 2024x + 2025}{x^{2} - x + 3} \right) + \frac{2}{e^{\pi x}} \left( \frac{x^{2023} + 2024x + 2025}{x^{2} - x + 3} \right) \).
Then the number of solutions of \( f(x) = 0 \) in \( \mathbb{R} \) is ________.
