4. It is known that the number $\cos 6^{0}$ is a root of the equation $32 t^{5}-40 t^{3}+10 t-\sqrt{3}=0$. Find the other four roots of this equation. (Answers in the problem should be compact expressions, not containing summation signs, ellipses, and radicals.)
Solution:

$\cos 5 x=16 \cos ^{5} x-20 \cos ^{3} x+5 \cos x$. Then the other roots of the equation will be the numbers $\cos 66^{\circ}, \cos 78^{\circ}, \cos 138^{\circ}, \cos 150^{\circ}$.

Answer: $\cos 66^{\circ}, \cos 78^{\circ}, \cos 138^{\circ}, \cos 150^{\circ}$