(4) If $\cos ^{5} \theta-\sin ^{5} \theta<7\left(\sin ^{3} \theta-\cos ^{3} \theta\right), \theta \in[0,2 \pi)$, then the range of $\theta$ is $\qquad$ .
(4) $\left(\frac{\pi}{4}, \frac{5 \pi}{4}\right)$ Hint: Inequality
$$
\cos ^{5} \theta-\sin ^{5} \theta\cos ^{3} \theta+\frac{1}{7} \cos ^{5} \theta \text {. }
$$

Also, $f(x)=x^{3}+\frac{1}{7} x^{5}$ is an increasing function on $(-\infty,+\infty)$, so $\sin \theta > \cos \theta$, hence
$$
2 k \pi+\frac{\pi}{4}<\theta<2 k \pi+\frac{5 \pi}{4}(k \in \mathbf{Z}) .
$$

Since $\theta \in[0,2 \pi)$, the range of $\theta$ is $\left(\frac{\pi}{4}, \frac{5 \pi}{4}\right)$.