could somebody please help me with equation ?

i think ive just made a stupid mistake because its not working T.T

Write general solution

tan2x = cot x

tan 2x = 2tanx/(1-tansquaredx)

therefore

2tanx/(1-tansquaredx) = 1/tanx

2tansquared x = 1/2

tan squared x = 1/4

tan x = + or - 1/2

which doesnt work

and the answers say the solution is npi + or - (pi/6)

thanks for any help !!