The set of all values of $\lambda$ for which the equation ${\cos }^{2}2x-2{\sin }^{4}x-2{\cos }^{2}x=\lambda$ has a real solution x, is

$\begin{array}{l}{\cos }^{2}2\mathrm{x}-2{\sin }^4\mathrm{x}-2{\cos }^2\mathrm{x}=\mathrm{\lambda }\\ \Rightarrow {\cos }^{2}2\mathrm{x}-\frac{1}{2}(1-\cos 2\mathrm{x}{)}^2-(1+\cos 2\mathrm{x})=\mathrm{\lambda }\\ \Rightarrow 2{\cos }^{2}2\mathrm{x}-\left(1+{\cos }^{2}2\mathrm{x}-2\cos 2\mathrm{x}\right)-2-2\cos 2\mathrm{x}=2\mathrm{\lambda }\\ \Rightarrow {\cos }^{2}2\mathrm{x}-3=2\mathrm{\lambda }\\ \therefore \mathrm{\lambda }\in \left[-\frac{3}{2},-1\right]\end{array}$