Solve tan2x=cot2x in the range 0-180

Tan(2x) ‒ 1/Tan(2x) = 0 \\ clear the denominators by multiplying both sides by Tan(2x) 

Tan²(2x) ‒ 1 = 0 as long as Tan(2x) exists and ≠ 0 

Tan²(2x) = 1 so Tan(2x) = -1 or Tan(2x) = 1 

Therefore, 2x = 45° or x = 22.5° or 2x = -45° or x = -22.5° 

There are many other values of x that work but not between -180° and 180°. 

Figure it out your self