Three Angular Bisectors Problem - 2

In triangle ABC, with angles β = /_ ABC  and γ = /_ BCA ,

three angular bisectors are drawn:

BD is the bisector of angle β = /_ ABC,

DE is the bisector of angle  /_ BDA, and

EF is the bisector of angle  /_ DEB.

Find the relation between angles β and γ, if bisector EF is parallel to side AC.

Relation between angles ABC and BCA is given here.