Find the number of roots of the equation `tan(x+pi/6)=2tanx ,forx in (0,3pi)dot`

Explanation

To find the number of roots of the equation \( \tan(x + \frac{\pi}{6}) = 2\tan x \) for \( x \) in the interval \( (0, 3\pi) \), we can follow these steps:

### Step 1: Rewrite the equation using the tangent addition formula
The tangent addition formula states that:
\[ \tan(a + b) = \frac{\tan a + \tan b}{1 - \tan a \tan b} \]
Applying this to our equation:
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