  Many experiments are being planned to measure the neutrino mixing parameter
$\theta_{13}$ using reactor as well as accelerator neutrino beams. In this
note, the theoretical significance of a high precision measurement of this
parameter is discussed. It is emphasized that it will provide crucial
information about different ways to understand the origin of large atmospheric
neutrino mixing and move us closer towards determining the neutrino mass
matrix. For instance if exact $\mu\leftrightarrow \tau$ symmetry in the
neutrino mass matrix is assumed to be the reason for maximal $\nu_\mu-\nu_\tau$
mixing, one gets $\theta_{13}=0$. Whether $\theta_{13}\simeq \sqrt{\Delta
m^2_{\odot}/\Delta m^2_A}$ or $\theta_{13}\simeq \Delta m^2_{\odot}/\Delta
m^2_A$ can provide information about the way the $\mu\leftrightarrow \tau$
symmetry breaking manifests in the case of normal hierarchy. We also discuss
the same question for inverted hierarchy as well as possible gauge theories
with this symmetry.
