Solve the general vlaue.
`tan 2x + 2 tan x =0`

Answer

To solve the equation \( \tan 2x + 2 \tan x = 0 \), we will follow these steps:

### Step 1: Use the double angle formula for tangent
The double angle formula for tangent is given by:
\[ \tan 2x = \frac{2 \tan x}{1 - \tan^2 x} \]
Substituting this into the equation, we get:
\[ \frac{2 \tan x}{1 - \tan^2 x} + 2 \tan x = 0 \]