解方程 $8\sin^2\theta+6\cos\theta+1=0$，其中 $0^\circ<\theta<180^\circ$。

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。

把正弦平方换成余弦平方。解出余弦后，只保留在余弦值域内的根。

Using $\sin^2\theta=1-\cos^2\theta$, the equation becomes $8\cos^2\theta-6\cos\theta-9=0$. This factors as

The value $\cos\theta=3/2$ is impossible. On the given interval, $\cos\theta=-3/4$ gives $\theta=138.6^\circ$ to one decimal place.