  The class of the two-axes pseudo-Finslerian metrics which is specified by the
condition of the angle-separation in the involved characteristic functions is
proposed and studied. The complete Total Set of algebraic and differential
equations is derived in all rigor which are necessary and sufficient in order
that a pseudo-Finsleroid metric function belong to the class. It proves
possible to solve the equations of the set. The angle-regular solution of the
Finsleroid-in-pseudo-Finsleroid type is found and described in detail.
