  The James Webb Space Telescope will allow to spectroscopically study an
unprecedented number of galaxies deep into the reionization era, notably by
detecting [OIII] and H$\beta$ nebular emission lines. To efficiently prepare
such observations, we photometrically select a large sample of galaxies at
$z\sim8$ and study their rest-frame optical emission lines. Combining data from
the GOODS Re-ionization Era wide-Area Treasury from Spitzer (GREATS) survey and
from HST, we perform spectral energy distribution (SED) fitting, using
synthetic SEDs from a large grid of photoionization models. The deep
Spitzer/IRAC data combined with our models exploring a large parameter space
enables to constrain the [OIII]+H$\beta$ fluxes and equivalent widths for our
sample, as well as the average physical properties of $z\sim8$ galaxies, such
as the ionizing photon production efficiency with
$\log(\xi_\mathrm{ion}/\mathrm{erg}^{-1}\hspace{1mm}\mathrm{Hz})\geq25.77$. We
find a relatively tight correlation between the [OIII]+H$\beta$ and UV
luminosity, which we use to derive for the first time the [OIII]+H$\beta$
luminosity function (LF) at $z\sim8$. The $z\sim8$ [OIII]+H$\beta$ LF is higher
at all luminosities compared to lower redshift, as opposed to the UV LF, due to
an increase of the [OIII]+H$\beta$ luminosity at a given UV luminosity from
$z\sim3$ to $z\sim8$. Finally, using the [OIII]+H$\beta$ LF, we make
predictions for JWST/NIRSpec number counts of $z\sim8$ galaxies. We find that
the current wide-area extragalactic legacy fields are too shallow to use JWST
at maximal efficiency for $z\sim8$ spectroscopy even at 1hr depth and JWST
pre-imaging to $\gtrsim30$ mag will be required.
