If $x\in \left[-{20}^0,-5^0\right]$ and $f\left(x\right)=\tan \left({50}^{\circ }+x\right)+\cos \left({50}^{\circ }+x\right)+\cot \left({50}^{\circ }+x\right)$ then global maximum value f(x) is k, then the value of [k² ] _________ 
(where [.] denotes greatest integer function).