$x + 2\tan x = {\pi \over 2}$ in [0, 2$\pi$] $2\tan x = {\pi \over 2} - x$ $2\tan x = {\pi \over 2} - x$ $\tan x = {\pi \over 4} - {x \over 2}$ $y = \tan x$ and $y = {{ - x} \over 2} + {\pi \over 4}$ 3 intersection points on the graph. $\therefore$ 3 solutions.