We normally aren't given double angle formulas for cotangents.
We usually only are given double angle formulas for tangents.

Since we know that , let's
convert to tangents:







We take reciprocals of both sides, and since the reciprocal
of 1 is 1, we have



We use the double-angle formula that we are always given:
which is 








Multiply both sides by the denominator on the left:



Solve for tan2(x)





Take square roots 





Remembering the special 30°-60°-90° right triangle:



we know by the ± that the angle can be in any quadrant
with a 30° reference angle, so the solutions are

30°, 150°, 210°, 330°  plus any integer n times 360°.

or in radians

,,, plus any integer n times .

Edwin