From the problem, we have an equation of :
[tex]2\tan ^2x+3\tan x+1=0[/tex]
Factor completely :
[tex](2\tan x+1)(\tan x+1)=0[/tex]
Equate both factors to 0 :
[tex]\begin{gathered} 2\tan x+1=0 \\ 2\tan x=-1 \\ \tan x=-\frac{1}{2} \\ x=\arctan (-\frac{1}{2}) \\ x=-26.565\ldots \end{gathered}[/tex][tex]\begin{gathered} \tan x+1=0 \\ \tan x=-1 \\ x=\arctan (-1) \\ x=\frac{1}{4}\pi,\frac{3}{4}\pi \end{gathered}[/tex]
The only exact values of x are π/4 and 3π/4
The answers are π/4 and 3π/4
