lf $f\left(x\right)={\left(-x\right)}^{\left[\frac{2x}{\pi }\right],}g\left(x\right)=\left|\sin x\right|-\left|\cos x\right|, \mathrm{and} \varphi \left(x\right)=f\left(x\right)g\left(x\right)$ (where [.] denotes the greatest integer function), then the respective fundamental periods of $f\left(x\right),g\left(x\right) \mathrm{and} \varphi \left(x\right)$ are