(3) The minimum value of the function $y=\sin ^{4} x+2 \sin x \cos x+\cos ^{4} x$ is
(3) From the problem, we know
$$
\begin{aligned}
y & =\left(\sin ^{2} x+\cos ^{2} x\right)^{2}+\sin 2 x-\frac{1}{2} \sin ^{2} 2 x \\
& =1+\sin 2 x-\frac{1}{2} \sin ^{2} 2 x \\
& =-\frac{1}{2}(\sin 2 x-1)^{2}+\frac{3}{2},
\end{aligned}
$$

Therefore, when $\sin 2 x=-1$, the function
$$
y=\sin ^{4} x+2 \sin x \cos x+\cos ^{4} x
$$

achieves its minimum value $y_{\text {min }}=-\frac{1}{2}$.