Consider triangle ABC, where angle B is a right angle. Points D and E are chosen on side BC in such a way that the consecutive angles BAD, DAE, and EAC measure 20 degrees, 15 degrees, and 20 degrees, respectively. Given that the length of segment EC is 3 units, your task is to determine the length of segment BD.

Triangle unfolds,

Angle B stands firm and strong.

Seeking D and E,

Consecutive angles revealed,

BD's mystery now pursued.

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