在 $0^\circ \leq \theta \leq 360^\circ$ 范围内，解方程 $4\sin^4\theta + 12\sin^2\theta - 7 = 0$。

先把 $\sin^2\theta$ 当作一个未知数。舍去不可能的平方值，再从正、负两个正弦值找出所有象限内的角。

Let $u=\sin^2\theta$, so $0\le u\le1$. Then

Only $u=\frac12$ is in range, giving $\sin\theta=\pm\frac{\sqrt2}{2}$. The reference angle is $45^\circ$. Both signs occur, so the solutions are $45^\circ$, $135^\circ$, $225^\circ$ and $315^\circ$.