Unexpected Substitutions

Geometry Level 3

Given \(x^2 + y^2 + z^2 + xyz = 4\) where \(x,y,z > 0\), evaluate \[\cos^{-1}(\frac{x}{2}) + \cos^{-1}(\frac{y}{2}) + \cos^{-1}(\frac{z}{2}) \]

rounded to the nearest integer.

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