How to solve this trigonometric equations?tan 2x cot x I need to factor this in order to sove for 0

tan2x*cotx - 3 = 0

We know
that: tan2x = sin2x/cos2x and cotx = cosx/sinx

==>
sin2x/cos2x *cosx/sinx = 3

Now we know that sin2x =
2sinx*cosx

==> 2sinxcosx/cos2x * cosx/sinx =
3

Reduce sinx:

==>
2cos^2 x/ cos2x = 3

Now we know that cos2x = 2cos^2
x-1

==> 2cos^2 x/(2cos^2 x -1) =
3

==> 2cos^2 x = 3(2cos^2 x
-1)

==> 2cos^2 x = 6cos^2 x -
3

==> -4cos^2 x=
-3

==> 4cos^2 x =
3

==> cos^2 x =
3/4

==> cosx = +-sqrt3/
2

==> x = pi/6, 5pi/6, 7pi/6, and
11pi/6