在 $-180^\circ < \theta < 180^\circ$ 范围内，解方程 $4\sin\theta\tan\theta = 1 + 5\cos\theta$。

把 $\tan\theta$ 改写为 $\sin\theta/\cos\theta$。乘以 $\cos\theta$ 后，用恒等式把方程化为关于余弦的二次式。

The equation is defined only when $\cos\theta\ne0$. Multiplying through by $\cos\theta$ gives

Using $\sin^2\theta=1-\cos^2\theta$, we obtain $9\cos^2\theta+\cos\theta-4=0$. Thus

Both values are in $(-1,1)$ and are nonzero. Cosine is even, so each principal angle and its negative lie in the required interval. The four solutions are $-136.4^\circ$, $-52.2^\circ$, $52.2^\circ$ and $136.4^\circ$.