$PT\Leftrightarrow tan x(3tan^2 x-1)+(1+sin x)(3+3tan^2 x)-4.(1+sin x)=0$$\Leftrightarrow tan x(3tan^2 x-1)+(1+sin x)(3tan^2 x-1)=0$
$\Leftrightarrow (3tan^2 x-1)(tan x+sin x+1)=0$
Với $tan x+sin x+1=0\Rightarrow sin x+cos x+sin x.cos x=0$
Đặt $sin x+cos x=t\Rightarrow sin x.cos x=\frac{t^2-1}{2}$