Let the bisectors of the exterior angles at \(B\) and \(C\) of triangle \(ABC\) meet at \(D\). Then, if all measurements are in degrees, find the value of angle \(BDC\). The original answer is in the form \(\frac{k}{m}(n - A)\). Please provide the value of k + m + n.

Let's think step by step and output the final answer within \boxed{}.
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