\begin{aligned} & \left(\alpha^2+\beta^2\right)^2-2 \alpha^2 \beta^2 \\ & {\left[(\alpha+\beta)^2-2 \alpha \beta\right]^2-2(\alpha \beta)^2} \\ & {\left[\frac{\cos ^2 \theta}{4}+1\right]^2-2 \cdot \frac{1}{4}} \\ & \left(\frac{\cos ^2 \theta}{4}+1\right)^2-\frac{1}{2} \\ & \mathrm{M}=\frac{25}{16}-\frac{1}{2}=\frac{17}{16} \\ & \mathrm{~m}=\frac{1}{2}, 16(\mathrm{M}+\mathrm{m})=25 \end{aligned}