解方程 $3\cot x-4\cot2x=3$，其中 $0^\circ\le x\le180^\circ$。

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。

用余切二倍角公式变成关于 $\cot x$ 的二次方程。原式不允许使 $\sin x$ 或 $\sin2x$ 为零的角。

The original equation excludes $x=0^\circ,90^\circ,180^\circ$.

Let $c=\cot x$. Using

the equation becomes

Multiplying by $c\ne0$,

so

Thus $\cot x=1$ or $\cot x=2$. On the stated interval, the valid angles are

Neither angle is excluded by the original equation.