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 values for $\theta$ is $\qquad$
4. $\left(\frac{\pi}{4}, \frac{5 \pi}{4}\right)$.

The given inequality is equivalent to
$$
7 \sin ^{3} \theta+\sin ^{5} \theta>7 \cos ^{3} \theta+\cos ^{5} \theta \text {. }
$$

Since $f(x)=7 x^{3}+x^{5}$ is an increasing function on $(-\infty,+\infty)$, it follows that $\sin \theta>\cos \theta$.
$$
\text { Hence } 2 k \pi+\frac{\pi}{4}<\theta<2 k \pi+\frac{5 \pi}{4}(k \in \mathbf{Z}) \text {. }
$$

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