  We investigate expected constraints on equilateral-type primordial
non-Gaussianities from future/ongoing imaging surveys, making use of the fact
that they enhance the halo/galaxy bispectrum on large scales. As model
parameters to be constrained, in addition to $f_{\rm NL}^{\rm equil}$, which is
related to the primordial bispectrum, we consider $g_{\rm NL}^{(\partial
\sigma)^4}$, which is related to the primordial trispectrum that appeared in
the effective field theory of inflation. After calculating the angular
bispectra of the halo/galaxy clustering and weak gravitational lensing based on
the integrated perturbation theory, we perform Fisher matrix analysis for three
representative surveys. We find that among the three surveys, the tightest
constraints come from Large Synoptic Survey Telescope ; its expected $1\sigma$
errors on $f_{\rm NL}^{\rm equil}$ and $g_{\rm NL}^{(\partial \sigma)^4}$ are
respectively given by $7.0 \times 10^2$ and $4.9 \times 10^7$. Although this
constraint is somewhat looser than the one from the current cosmic microwave
background observation, since we obtain it independently, we can use this
constraint as a cross check. We also evaluate the uncertainty with our results
caused by using several approximations and discuss the possibility to obtain
tighter constraint on $f_{\rm NL}^{\rm equil}$ and $g_{\rm NL}^{(\partial
\sigma)^4}$.
