Neutrino oscillations: measuring $\theta_{13}$ including its sign

In neutrino phenomenology, terms in the oscillation probabilities linear in $\sin \theta_{13}$ lead naturally to the question ``How can one measure $\theta_{13}$ including its sign?'' Here we demonstrate analytically and with a simulation of neutrino data that ${\mathcal P}_{e\mu}$ and {\mathcal {P}_{\mu\mu} at $L/E = 2\pi/\Delta_{21}$ exhibit significant linear dependence on $\theta_{13}$ in the limit of vacuum oscillations. Measurements at this particular value of $L/E$ can thus determine not only $\theta_{13}$ but also its sign, if CP violation is small.