$If {\sin }^4\theta + {\cos }^4\theta = \mathcal{l}+3+ k {\sin }^2\theta {\cos }^2\theta then$

$$\begin{gathered} \left({\sin }^4\mathrm{\theta }+{\cos }^4\mathrm{\theta }\right)=\mathrm{l}+3+\mathrm{k} {\sin }^2\mathrm{\theta } {\cos }^2\mathrm{\theta } \\ {\left({\sin }^2\mathrm{\theta }+{\cos }^2\mathrm{\theta }\right)}^2-2{\sin }^2\mathrm{\theta } {\cos }^2\mathrm{\theta } \\ =\mathrm{l}+3+\mathrm{k} {\sin }^2\mathrm{\theta } {\cos }^2\mathrm{\theta } \\ 1-2{\sin }^2\mathrm{\theta } {\cos }^2\mathrm{\theta }=\mathrm{l}+3+\mathrm{k} {\sin }^2\mathrm{\theta } {\cos }^2\mathrm{\theta } \\ \mathrm{l}+3=1 \Rightarrow \mathrm{l}=-2 \\ \mathrm{k}=-2 \\ \mathrm{l}-\mathrm{k}=0 \end{gathered}$$