For xϵ ( 0, (3)/(2) ) , let f(x) = x , g(x) = x and h(x) = 1 - x ^...

$f\left(x\right) = \sqrt{x}$

$g\left(x\right) = \tan x$

$h\left(x\right) = \dfrac{1 - {x}^{2}}{1 + {x}^{2}}$
$fog\left(x\right) = \sqrt{\tan x}$
$hofog\left(x\right) = h\left(\sqrt{\tan x}\right)$

$= \dfrac{1 - \tan x}{1 + \tan x} = \tan \left(\dfrac{\pi}{4} - x\right)$
$ϕ\left(x\right) = \tan \left(\dfrac{\pi}{4} - x\right)$
$ϕ\left(\dfrac{\pi}{3}\right) = \tan \left(\dfrac{\pi}{4} - \dfrac{\pi}{3}\right)$

$= \tan \left(- \dfrac{\pi}{12}\right) = - tan\dfrac{\pi}{12}$

$= \tan \left(\pi - \dfrac{\pi}{12}\right) = tan\dfrac{11\pi}{12}$