# How to calculate this integration accurately

I need to calculate this integration:

$$int_0^{2 pi}int_0^{2 pi}int_0^{2 pi} F(x,y,z)$$

which:

$$F(x,y,z)=left{ begin{array}{rcl} f(x,y,z)^2 & & {0 leq f(x,y,z)}\ 0 & & {True} end{array} right.$$

$$f(x,y,z)=sin (x+y)-sin (x+z)-cos (y-z)$$

Firstly I tried to calculate this integration by using `NIntegrate`. it is not work.

``````p = 2*Pi;
f(x_, y_, z_) := Sin(x + y) - Cos(y - z) - Sin(x + z);
P = ImplicitRegion(f(x, y, z) >= 0, {{x, 0, p}, {y, 0, p}, {z, 0, p}});
NIntegrate(f(x, y, z)^2, Element({x, y, z} , P))
(*NIntegrate(f(x,y,z)^2,{x,y,z}(Element)P)*)

``````

Then i can get result after setting the option `Method -> "MonteCarlo"`,but the question is that the result is not stable.
so what can i do to get the accurate result.any suggestions will be greatly appreciated.