4. Calculate $\cos 2016^{\circ}=$
4. $-\frac{\sqrt{5}+1}{4}$.

Notice that, $\cos 2016^{\circ}=-\cos 36^{\circ}$.
By $\sin 36^{\circ}=\cos 54^{\circ}$
$$
\begin{aligned}
\Rightarrow & 2 \sin 18^{\circ} \cdot \cos 18^{\circ} \\
& =\cos 36^{\circ} \cdot \cos 18^{\circ}-\sin 36^{\circ} \cdot \sin 18^{\circ} \\
& =\cos 36^{\circ} \cdot \cos 18^{\circ}-2 \sin ^{2} 18^{\circ} \cdot \cos 18^{\circ} \\
\Rightarrow & 2 \sin 18^{\circ}=\cos 36^{\circ}-2 \sin ^{2} 18^{\circ}=1-4 \sin ^{2} 18^{\circ} \\
\Rightarrow & \sin 18^{\circ}=\frac{\sqrt{5}-1}{4} \\
\Rightarrow & \cos 36^{\circ}=1-2 \sin ^{2} 18^{\circ}=\frac{\sqrt{5}+1}{4} \\
\Rightarrow & \cos 2016^{\circ}=-\frac{\sqrt{5}+1}{4} .
\end{aligned}
$$