In triangle $ABC,$ $\angle C = \frac{\pi}{2}.$  Find
\[\arctan \left( \frac{a}{b + c} \right) + \arctan \left( \frac{b}{a + c} \right).\]
Question:
In triangle $ABC,$ $\angle C = \frac{\pi}{2}.$  Find
\[\arctan \left( \frac{a}{b + c} \right) + \arctan \left( \frac{b}{a + c} \right).\]
Answer:
Let's think step by step.

user
\frac{\pi}{4}
In triangle $ABC,$ $\angle C = \frac{\pi}{2}.$  Find
\[\arctan \left( \frac{a}{b + c} \right) + \arctan \left( \frac{b}{a + c} \right).\]
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