Cotangent is the reciprocal of the tangent:



Multiply both sides by tan(135°-2y):
 


Divide both sides by -0.5:



Simplify left side:



Use formula for tan(A-B):



Use the fact that tan(135°) = -1, substituting:



Simplify:



Multiply both sides by 1-tan(2y):



Distribute on the left:



Add +2 to both sides:



Add + tan(2y) to both sides:



Divide both sides by 3:



Use formula for tan(2θ):



Cross-multiply:



Get 0 on the right:



Use quadratic formula:



Simplify:















Using the + :





  <-- 1st quadrant solution

Add 180° to get the 3rd quadrant solution:

  <-- 3rd quadrant solution

Using the - :





  <-- 4th quadrant negative solution

which calculator always gives but which we cannot accept here
since it's not between 0° and 360°.

So we add 360° to get an equivalent positive 4th quadrant 
solution which is between 0° and 360:

  <-- 4th quadrant solution

Subtract 180° to get the 2nd quadrant solution:

  <-- 2nd quadrant solution

So there are 4 solutions between 0° and 360°.

Edwin