解方程 $3\cot\theta-4\operatorname{cosec}^2\theta+5=0$，其中 $-\pi\le\theta\le\pi$。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

用余割与余切的平方关系化为二次方程，逐个列出指定区间内的角。

Using $\operatorname{cosec}^2\theta=1+\cot^2\theta$,

so

Factoring,

For $\cot\theta=1$, the solutions in $[-\pi,\pi]$ are $\theta=\pi/4$ and $\theta=-3\pi/4$.

For $\cot\theta=-1/4$, $\tan\theta=-4$, giving

and

Therefore

The values $-\pi,0,\pi$ are excluded because the original cotangent and cosecant are undefined there.