  To explain the linear polarization observed in spatially resolved structures
in the solar atmosphere, the solution of polarized radiative transfer (RT)
equation in multi-dimensional (multi-D) geometries is essential. For strong
resonance lines partial frequency redistribution (PRD) effects also become
important. In a series of papers we have been investigating the nature of
Stokes profiles formed in multi-D media including PRD in line scattering. For
numerical simplicity so far we restricted our attention to the particular case
of PRD functions which are averaged over all the incident and scattered
directions. In this paper we formulate the polarized RT equation in multi-D
media that takes into account Hanle effect with angle-dependent PRD functions.
We generalize here to the multi-D case, the method of Fourier series expansion
of angle-dependent PRD functions originally developed for RT in 1D geometry. We
show that the Stokes source vector $\bm{S}=(S_I,S_Q,S_U)^T$ and the Stokes
vector $\bm{I}=(I,Q,U)^T$ can be expanded in terms of infinite sets of
components ${\tilde{\bm{\mathcal{S}}}}^{(k)}$,
${\tilde{\bm{\mathcal{I}}}}^{(k)}$ respectively, $k\in[0,+\infty)$. We show
that the components ${\tilde{\bm{\mathcal{S}}}}^{(k)}$ become independent of
the azimuthal angle ($\varphi$) of the scattered ray, whereas the components
${\tilde{\bm{\mathcal{I}}}}^{(k)}$ remain dependent on $\varphi$ due to the
nature of RT in multi-D geometry. We also establish that
${\tilde{\bm{\mathcal{S}}}}^{(k)}$ and ${\tilde{\bm{\mathcal{I}}}}^{(k)}$
satisfy a simple transfer equation, which can be solved by any iterative method
like an Approximate Lambda Iteration (ALI) or a Biconjugate-Gradient type
projection method provided we truncate the Fourier series to have a finite
number of terms.
