(2) If two acute angles $\alpha, \beta$ satisfy: $(\sin \alpha+\cos \alpha)(\sin \beta+\cos \beta)=2$, then $(\sin 2 \alpha+\cos 3 \beta)^{2}+(\sin 2 \beta+\cos 3 \alpha)^{2}=$ $\qquad$ .
(2) $3-2 \sqrt{2}$ Hint: The conditional equation can be transformed into: $\sin (\alpha+\beta)+\cos (\alpha-\beta)=2$, so $\sin (\alpha+\beta)=\cos (\alpha-\beta)=1$, therefore $\alpha+\beta=90^{\circ}, \alpha=\beta$, thus $\alpha=$ $\beta=45^{\circ}$, then $(\sin 2 \alpha+\cos 3 \beta)^{2}+(\sin 2 \beta+\cos 3 \alpha)^{2}=2\left(\sin 90^{\circ}+\right.$ $\left.\cos 135^{\circ}\right)^{2}=3-2 \sqrt{2}$.