The more easily to induce witnesses to testify, we are conducting our hearings in private.
jest parafrazą zdania:
In order to more easily induce witnesses to testify, we are conducting our hearings in private.
Proszę o pomoc.
The adverbial "the" (always) precedes a comparative. Your "in order to" is purposive and implies no comparison.
There is only one "the" in your examples and that's perhaps why the sense of this single "the" may seem unclear. To show the comparison (and the co-respondence intrinsic to comparisons), try paraphrasing the pithy "the sooner the better."
To get you going, I can expand for you the equally pithy "the more the merrier": by how much we are more, by so much we shall be merrier.