  Modern trends in beam-driven radiation sources involve interaction of
Cherenkov wakefields with open-ended circular waveguide structures having
complicated dielectric lining, with a three-layer dielectric capillary recently
offered for reducing the radiation divergency being a representative example
\cite{Jiang2020}. This paper presents rigorous approach allowing analytical
description of electromagnetic processes occuring when the described structure
is excited by single waveguide mode. In other words, corresponding canonical
waveguide diffraction problem is considered in rigorous formulation. This is
continuation of our recent paper \cite{GV2022} where a simpler case of a
two-layer dielectric filling has been considered. Here we use the same
analytical approach based on Wiener-Hopf-Fock technique and deal with more
complicated case of a three-layer dielectric lining.
