  In this article, we perform a deep analysis of the Bianchi identities in the
two known formulations developed for the four-dimensional effective type IIA
supergravity theory with (non-)geometric fluxes. In what we call the `first
formulation', fluxes are expressed in the real six-dimensional indices while in
the `second formulation', fluxes are written in the cohomology form. We find
that the set of flux constraints arising from these two known formulations are
not equivalent, and there are missing identities in the cohomology version
which need to be supplemented to match with the first formulation. By analyzing
two explicit examples, we conjecture a model independent form for (the most of)
the missing identities. These identities have been mostly overlooked in the
previous attempts of studying moduli stabilization, particularly for the models
developed in the beyond toroidal frameworks, where they could play some
important role.
