Find the number of solution of `2tan^(-1)(tanx)=6-xdot`

Explanation

To solve the equation \( 2\tan^{-1}(\tan x) = 6 - x \), we will find the number of solutions step by step.

### Step 1: Understand the function \( \tan^{-1}(\tan x) \)

The function \( \tan^{-1}(\tan x) \) is equal to \( x \) for \( x \) in the interval \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \) and can be expressed as:
\[ \tan^{-1}(\tan x) = x - n\pi \quad \text{for } n \in \mathbb{Z} \]
...