Applying the Resonance Method to $\textrm{Re}\left(e^{-i\theta}\log\zeta(\sigma+it)\right)$

We apply the resonance method to Montgomery's convolution formula for $\textrm{Re}\left(e^{-i\theta}\log\zeta(\sigma+it)\right)$ in the strip $1/2 < \sigma < 1$. This gives new insight into maximal values of $\textrm{Re}\left(e^{-i\theta}\log\zeta(\sigma+it)\right)$ for $t \in [T^{\beta},T]$ for all $\beta \in (0,1)$ and real $\theta$.