See the diagram below.

I will not use three letters to describe an angle, i'll use one.

Let O be angle BOC

Let be angle BAC

Let C be angle ACB

Let B be angle ABC

We want to find angle O (the red angle) in terms of

Remember that all angles in a triangle add up to , and that bisecting an angle means dividing it into two equal parts.

So, for we must have that:

.................(1)

Now for we must have:

Now substitute the expression for B + C from equation (1), we get: