3.4. For what least positive $a$ is the inequality $\frac{\sqrt[3]{\sin ^{2} x}-\sqrt[3]{\cos ^{2} x}}{\sqrt[3]{\operatorname{tg}^{2} x}-\sqrt[3]{\operatorname{ctg}^{2} x}}<\frac{a}{2}$ satisfied for all permissible $x \in\left(\frac{3 \pi}{2} ; 2 \pi\right)$? Round the answer to the nearest hundredths if necessary.
Answer: 0.79 (exact value: $\frac{1}{\sqrt[3]{2}}$ ).