Solve `tan2x=-cot(x+pi/3)`

Explanation

To solve the equation \( \tan(2x) = -\cot\left(x + \frac{\pi}{3}\right) \), we can follow these steps:

### Step 1: Rewrite the cotangent function
We know that \( \cot \theta = \frac{1}{\tan \theta} \). Therefore, we can rewrite the equation as:
\[ \tan(2x) = -\cot\left(x + \frac{\pi}{3}\right) = -\frac{1}{\tan\left(x + \frac{\pi}{3}\right)} \]

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