  We consider the distribution of $\arg\zeta(\sigma+it)$ on fixed lines $\sigma
> \frac12$, and in particular the density \[d(\sigma) = \lim_{T \rightarrow
+\infty}
  \frac{1}{2T}
  |\{t \in [-T,+T]: |\arg\zeta(\sigma+it)| > \pi/2\}|\,,\] and the closely
related density \[d_{-}(\sigma) = \lim_{T \rightarrow +\infty}
  \frac{1}{2T}
  |\{t \in [-T,+T]: \Re\zeta(\sigma+it) < 0\}|\,.\] Using classical results of
Bohr and Jessen, we obtain an explicit expression for the characteristic
function $\psi_\sigma(x)$ associated with $\arg\zeta(\sigma+it)$. We give
explicit expressions for $d(\sigma)$ and $d_{-}(\sigma)$ in terms of
$\psi_\sigma(x)$. Finally, we give a practical algorithm for evaluating these
expressions to obtain accurate numerical values of $d(\sigma)$ and
$d_{-}(\sigma)$.
