Example 2. Simplify $\sin ^{3} 10^{\circ}+\sin ^{3} 30^{\circ}+\sin 50^{\circ}$ $+\sin ^{3} 70^{\circ}$.
Apply the formula
$$
\begin{array}{l}
\sum_{i=1}^{n} \sin ^{3} a_{0} \\
=\frac{3 \sin \left(a_{1}+\frac{n-1}{2} d\right) \sin \frac{n}{2} d}{4 \sin \frac{d}{2}} \\
-\frac{\operatorname{sins}\left(a_{1}+\frac{n-1}{2} d\right) \sin \frac{3 n}{2} d}{4 \sin \frac{3 d}{2}}
\end{array}
$$

It is known that the original expression equals $\frac{3}{8}\left(\frac{1}{\sin 10^{\circ}}-2\right)$. (Author's unit: Kaifeng Educational College)

Kao Wen Yu
[1] Han Shizhong, Several Trigonometric Formulas and Their Applications, *Mathematical Communications* 1981, No. 5.