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
Solve:
$$
\cos ^{5} \theta-\sin ^{5} \theta<7\left(\sin ^{3} \theta-\cos ^{3} \theta\right) \Rightarrow \cos ^{5} \theta+7 \cos ^{3} \theta<\sin ^{5} \theta+7 \sin ^{3} \theta .
$$

Construct the function $f(x)=x^{5}+7 x^{3} \Rightarrow f^{\prime}(x)=5 x^{4}+21 x^{2} \geqslant 0 \Rightarrow f(x)$ is a monotonically increasing function on $\mathbf{R}$, combining with $\theta \in[0,2 \pi)$, so $\cos \theta<\sin \theta \Rightarrow \theta \in\left(\frac{\pi}{4}, \frac{5 \pi}{4}\right)$.