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Post Reopened by Igor Rivin, Yemon Choi, Alexey Ustinov, Carlo Beenakker, Neil Strickland

What is the value of this triple integral $$\int_0^{2\pi}\int_0^{2\pi}\int_0^{2\pi}|\cos x+\cos y+\cos z|dxdydz?$$$$\int\limits_0^{2\pi}\int\limits_0^{2\pi}\int\limits_0^{2\pi}|\cos x+\cos y+\cos z|\ dx\ dy\ dz?$$ It has to do with some Schwarz lemma.

What is the value of this triple integral $$\int_0^{2\pi}\int_0^{2\pi}\int_0^{2\pi}|\cos x+\cos y+\cos z|dxdydz?$$ It has to do with some Schwarz lemma.

What is the value of this triple integral $$\int\limits_0^{2\pi}\int\limits_0^{2\pi}\int\limits_0^{2\pi}|\cos x+\cos y+\cos z|\ dx\ dy\ dz?$$ It has to do with some Schwarz lemma.

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An interesting triple integral

What is the value of this triple integral $$\int_0^{2\pi}\int_0^{2\pi}\int_0^{2\pi}|\cos x+\cos y+\cos z|dxdydz?$$ It has to do with some Schwarz lemma.