Prove that `(tan3x)/(tanx)` never lies between `1/3a n d3` .

Explanation

To prove that \(\frac{\tan 3x}{\tan x}\) never lies between \(\frac{1}{3}\) and \(3\), we will start by using the formula for \(\tan 3x\).

### Step 1: Write the formula for \(\tan 3x\)
The formula for \(\tan 3x\) is given by:
\[ \tan 3x = \frac{3\tan x - \tan^3 x}{1 - 3\tan^2 x} \]

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