Solve `tan x+tan 2x+tan 3x = tan x tan 2x tan 3x, x in [0, pi]`.

Explanation

To solve the equation \( \tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x \) for \( x \) in the interval \([0, \pi]\), we can use a known identity for the tangent function.

### Step-by-step Solution:

1. **Recognize the Identity**:
We know that the equation \( \tan a + \tan b + \tan c = \tan a \tan b \tan c \) holds true when \( a + b + c = n\pi \) for some integer \( n \). Here, we can set \( a = x \), \( b = 2x \), and \( c = 3x \).

2. **Set Up the Equation**:
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