Let $f \left(x\right) = \left[{\tan }^{2}x\right] \left[co{t}^{2}x\right],$ then find the number of points at which $f \left(x\right)$is discontinuous in $(0,2\mathrm{\pi }).$

Note:$\left[k\right]$ denotes greatest integer function less than or equal to $k.$