[tex]\bf \stackrel{\stackrel{notice~~ax^2+bx+c=0}{\downarrow }}{\underset{\textit{tis just a quadratic}}{cot^2(x)+2cot(x)+1=0}}\implies [cot(x)+1][cot(x)+1]=0 \\\\\\ cot(x)+1=0\implies cot(x)=-1\implies cot^{-1}[cot(x)]=cot^{-1}(-1) \\\\\\ x=cot^{-1}(-1)\implies x= \begin{cases} \stackrel{II~Quadrant}{\frac{3\pi }{4}}\\[1em] \stackrel{IV~Quadrant}{\frac{7\pi }{4}} \end{cases}[/tex]
