Triple integral in the first octant

Calculus Level 4

What is the value of Rcos(x+y+z) dx dy dz \iiint_R \cos (x + y + z)\ dx\ dy\ dz, where RR is the region bounded by x0x \geq 0, y0y \geq 0, z0z \geq 0 and x+y+z2πx + y + z \leq 2\pi?

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