  Effects of the 1-3 leptonic mixing on the solar neutrino observables are
studied and the signatures of non-zero $\theta_{13}$ are identified. For this
we have re-derived the formula for $3\nu$-survival probability including all
relevant corrections and constructed the iso-contours of observables in the
$\sin^2 \theta_{12} - \sin^2 \theta_{13}$ plane. Analysis of the solar neutrino
data gives $\sin^2\theta_{13} = 0.007^{+ 0.080}_{-0.007}$ (90% C.L.) for
$\Delta m^2 = 8 \cdot 10^{-5}$ eV$^2$. The combination of the ratio CC/NC at
SNO and gallium production rate selects $\sin^2\theta_{13} = 0.017 \pm 0.026$
($1\sigma$). The global fit of all oscillation data leads to zero best value of
$\sin^2 \theta_{13}$. The sensitivity ($1\sigma$ error) of future solar
neutrino studies to $\sin^2 \theta_{13}$ can be improved down to 0.01 - 0.02 by
precise measurements of the pp-neutrino flux and the CC/NC ratio as well as
spectrum distortion at high ($E > 4$ MeV) energies. Combination of experimental
results sensitive to the low and high energy parts of the solar neutrino
spectrum resolves the degeneracy of angles $\theta_{13}$ and $\theta_{12}$.
Comparison of $\sin^2 \theta_{13}$ as well as $\sin^2 \theta_{12}$ measured in
the solar neutrinos and in the reactor/accelerator experiments may reveal new
effects which can not be seen otherwise.
