(6 points) Plain Monte Carlo integration
∫0π dx/π ∫0π dy/π ∫0π dz/π [1-cos(x)cos(y)cos(z)]-1 = Γ(1/4)4/(4π3) ≈ 1.3932039296856768591842462603255This is a difficult singular integral, do not use it for your tests and error estimates, use something less sungular.
(3 points)
O(1/√N)
.
(1 point)