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 follow these steps:

### Step 1: Recognize the identity
We know from trigonometric identities that:
\[ \tan A + \tan B + \tan C = \tan A \tan B \tan C \quad \text{if and only if} \quad A + B + C = n\pi \]
for some integer \( n \). Here, we can let \( A = x \), \( B = 2x \), and \( C = 3x \).
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