Mark the Correct alternative in the following:

In (0, π), the number of solutions of the equation tan x + tan 2x + tan 3x = tan x tan 2x tan 3x is

tan x+tan2x+tan3x -tan xtan2xtan3x=0

tan x + tan2x + tan3x (1-tan xtan2x) = 0

tan x + tan2x = -tan3x (1-tan xtan2x)

tan 3x=-tan3x

2 tan3x=0

tan 3x=0

3x=2nπ

For

n=0, x=0

n=1,

so, there are only two possible solutions

Option D