Solve for an Angle

$3 sec^2 (x) - 2\sqrt{3} tan (x) - 6 = 0$

Using the identity sec^2(x) = 1+tan^2(x)

$3(1+tan^2(x)) - 2\sqrt{3} tan (x) - 6 = 0$

$3tan^2(x) - 2\sqrt{3} tan (x) - 3 = 0$

$3tan^2(x) - 2\sqrt{3} tan (x) - 3 = 0$

$(3tan^2(x)+\sqrt{3})(tan^2(x)-\sqrt{3})=0$

$tan(x)=\sqrt{-\sqrt{3}/3}$

$no \space solution$

$tan(x)=\sqrt[4]{3}$

$x=52.8°\space or \space 233°$