If \(\rm \int\frac{1-(cot\ x)^{2019}}{ \tan x+( cot\ x)^{2020}}dx=\frac{1}{n}\ In \begin{vmatrix} (f(x))^n+(g(x))^n \end{vmatrix}+c\), then the value of \(\rm n\begin{bmatrix} (f(x))^4+)g(x))^4 \end{bmatrix}_{x=\frac{\pi}{3}}=\)