\(9+\cot^2x=12\)
\(\cot^2x=3\)
\(\cot x=\pm\sqrt3\)
\(\tan x=\pm\dfrac1{\sqrt3}\)
This happens on the unit circle whenever \(x=\dfrac\pi6,\dfrac{5\pi}6,\dfrac{7\pi}6,\dfrac{11\pi}6\), and more generally for \(x=\dfrac\pi6+n\pi\) and \(x=-\dfrac\pi6+n\pi\) for integers \(n\).
