A simple problem in a package

Calculus Level 3

Let \(x_1, x_2, x_3, \ldots\) be roots of the function \[f(x) = \sin{\left( \dfrac{\pi \ln{(x)}}{\ln3} \right)}\] where \(1 < x_1 < x_2 < x_3 < \cdots\).

What is the value of \[\sum_{n=1}^{\infty} \dfrac{1}{x_n} \quad ? \]