If $g\left(x\right)=f({\mathrm{tan}}^{2}x-2\mathrm{tan}x+4),\text{}0x\frac{\pi}{2}$ , then g(x) is increasing in what interval?

I have first differentiated the given equation and found the value of x for which the interior part of f is 3 ,this gives$x=\frac{\pi}{4}$ and it gives me $g\left(\frac{\pi}{4}\right)=0$ but I am stuck here and don't know what to do after this.

I have first differentiated the given equation and found the value of x for which the interior part of f is 3 ,this gives