If $\frac{\cos 3x}{\cos x} = \frac{1}{3},$ then determine $\frac{\sin 3x}{\sin x}.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $\frac{\cos 3x}{\cos x} = \frac{1}{3},$ then determine $\frac{\sin 3x}{\sin x}.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{7}{3}
If $\frac{\cos 3x}{\cos x} = \frac{1}{3},$ then determine $\frac{\sin 3x}{\sin x}.$
train