A function $f(x)$ is defined such that its derivative is $f'(x) = \frac{\tan^{-1}(x)}{x}$ for $x > 0$. If $f(1) = 0$, determine the value of $f(0)$ by evaluating the definite integral $\int_0^1 \frac{\tan^{-1}(x)}{x} dx$ expressed as an infinite series.