  We use a new approach to derive dielectric mixing rules for macroscopically
homogeneous and isotropic multicomponent mixtures of anisotropic inhomogeneous
dielectric particles. Two factors of anisotropy are taken into account, the
shape of the particles and anisotropy of the dielectric parameters of the
particles' substances. Our approach is based upon the notion of macroscopic
compact groups of particles and the procedure of averaging of the fields over
volumes much greater than the typical scales of these groups. It enables us to
effectively sum up the contributions from multiple interparticle reemission and
short-range correlation effects, represented by all terms in the infinite
iterative series for the electric field strength and induction. The expression
for the effective permittivity can be given the form of the Lorentz-Lorenz
type, which allows us to determine the effective polarizabilities of the
particles in the mixture. These polarizabilities are found as integrals over
the regions occupied by the particles and taken of explicit functions of the
principal components of the permittivity tensors of the particles' substances
and the permittivity of the host medium. The case of a mixture of particles of
the ellipsoidal shape is considered in detail to exemplify the use of general
formulas. As another example, Bruggeman-type formulas are derived under
pertinent model assumptions. The ranges of validity of the results obtained are
discussed as well.
