If \( \cos^{-1}\alpha + \cos^{-1}\beta + \cos^{-1}\gamma = 3\pi \), then \( \alpha(\beta+\gamma) + \beta(\gamma+\alpha) + \gamma(\alpha+\beta) \) is equal to:
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For inverse trigonometric sums:
Always recall principal value ranges.
If sum equals maximum possible value, each term must be maximal.
\( \cos^{-1}x = \pi \Rightarrow x = -1 \)