The value of f(x) = x⁴ + 4x³ + 2x² - 4x + 7 , when $\mathrm{x}=\cot \frac{11\mathrm{\pi }}{8}$ is _______ .

$\begin{array}{l}\mathrm{x}=\cot \frac{11\mathrm{\pi }}{8}=\cot \left(\mathrm{\pi }+\frac{3\mathrm{\pi }}{8}\right)=\cot \frac{3\mathrm{\pi }}{8}=\sqrt{2}-1\\ \Rightarrow (\mathrm{x}+1{)}^2=2\\ \therefore {\mathrm{x}}^2+2\mathrm{x}-1=0\end{array}$
Now, 
$\begin{array}{l}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^4+4{\mathrm{x}}^3+2{\mathrm{x}}^2-4\mathrm{x}+7\\ ={\mathrm{x}}^2\left({\mathrm{x}}^2+2\mathrm{x}-1\right)+2{\mathrm{x}}^3+3{\mathrm{x}}^2-4\mathrm{x}+7\\ =0+2{\mathrm{x}}^3+3{\mathrm{x}}^2-4\mathrm{x}+7\\ =2\mathrm{x}\left({\mathrm{x}}^2+2\mathrm{x}-1\right)-{\mathrm{x}}^2-2\mathrm{x}+7\\ =-{\mathrm{x}}^2-2\mathrm{x}+7\\ =-\left({\mathrm{x}}^2+2\mathrm{x}-1\right)+6\end{array}$