Triple integral in the first octant

Calculus Level 4

What is the value of \( \iiint_R \cos (x + y + z)\ dx\ dy\ dz\), where \(R\) is the region bounded by \(x \geq 0\), \(y \geq 0\), \(z \geq 0\) and \(x + y + z \leq 2\pi\)?

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