在 $-180^\circ < \theta < 180^\circ$ 范围内，解方程 $6\sin\theta = 1 + \frac{2}{\sin\theta}$。

原式要求 $\sin\theta\ne0$。乘以 $\sin\theta$ 后解二次方程，再根据两个正弦值的符号找齐角度。

Multiplication by $\sin\theta$ gives

For $\sin\theta=-\frac12$, the two angles in the interval are $-150^\circ$ and $-30^\circ$. For $\sin\theta=\frac23$, the principal angle is $\alpha=\sin^{-1}(2/3)$ and the other is $180^\circ-\alpha$. These give $41.8^\circ$ and $138.2^\circ$. All four have nonzero sine.