Three Angular Bisectors

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

EC is the bisector of angle  /_ DEB.

Find the relation between angles β and γ.

Check the case  β = π/6,  γ = ¾ π.

Find other “simple” cases.

Relation between angles ABC and BCA is given here.