Precalculus of algebra – Find angles from the side length in the previous calculation

I had this problem on a college test recently. I had no idea how to do it, and I lost all my points for it. I assumed it would have something to do with finding the correct values ​​for the sides and angles of a triangle given the rules of sine and cosine, but the problem did not seem to have enough space to solve them with that.

In my exam my teacher wrote the identity of the addition of the tangent:

$$ tan (A + B) = frac { tan (A) + tan (B)} {1 – tan (A) cdot tan (B)} $$

But I'm not sure how relevant this is.

If C = A + B, find the tan (C)
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