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\begin{equation*}
  \arg{G(i\omega_0)} = 
  \frac{\pi}{2} \int_0^\infty f(\omega)
    \frac{d\log{|G(i\omega)|}}{d\log{\omega}}\, d\log{\omega} \approx
    \frac{\pi}{2} \left. \frac{d\log{|G(i\omega)|}}{d\log{\omega}} \right|_{\color{blue}\omega = \omega_0}
\end{equation*}
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