maths trigonometry

(=^o^=)
Yuki, nice question!!!

(1)
Note that AB // DC.

(2)
Then, you can know that △ABE ~ △DCE (AAA)

(3)
By similar triangle, you know that
BE : DE = AB : DC (this is what you are asked)

(4)
Note that tan φ = AB/BC
tan θ = DC / BC

(5)
Therefore,
BE : DE = AB : DC = AB/BC : DC/BC = tan φ : tan θ