\arctan x=x-\frac{x^3}{3}+\mathcal{O}_0(x^5) \newline
\frac{\arctan x}{x}=1-\frac{x^2}{3}+\mathcal{O}_0(x^4) \newline
\ln (\frac{\arctan x}{x})=\ln (1-(\frac{x^2}{3}+\mathcal{O}_0(x^4)))=-\frac{x^2}{3}+\mathcal{O}_0(x^8) \newline
\frac{\ln(\frac{\arctan x}{x})}{x^2}=-\frac{1}{3}+\mathcal{O}_0(x^6)