  The lack of clarity of various mode-coupling theory (MCT) approximations,
even in equilibrium,makes it hard to understand the relation between various
MCT approaches for sheared steady states as well as their regime of validity.
Here we try to understand these approximations indirectly by deriving the MCT
equations through two different approaches for a colloidal system under shear,
first, through a microscopic approach, as suggested by Zaccarelli et al, and
second, through fluctuating hydrodynamics, where the approximations used in the
derivation are quite clear. The qualitative similarity of our theory with a
number of existing theories show that linear response theory might play a role
in various approximations employed in deriving those theories and one needs to
be careful while applying them for systems arbitrarily far away from
equilibrium, such as a granular system or when shear is very strong. As a
byproduct of our calculation, we obtain the extension of Yvon-Born-Green (YBG)
equation for a sheared system and under the assumption of random-phase
approximation, the YBG equation yields the distorted structure factor that was
earlier obtained through different approaches.
