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) $


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))

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.