We have, `cot x + tan x = 2 cosec x`

`therefore" "(cosx)/(sinx) +(sinx)/(cosx) = (2)/(sin x)`

`rArr" "(cos^(2)x +sin^(2)x)/(sin xcosx) = (2)/(sinx)`

`rArr " "(cos^(2)x + sinx^(2)x)/(sin x cos x) = (2)/(sinx)`

`rArr" "(1)/(sinx cos x) = (2)/(sinx)`

`rArr" "(1)/(cos x) = 2 " "(because sin x ne 0)`

`therefore" "cosx = (1)/(2)`

`rArr" "cosx = cos.(pi)/(2)`

The general solution of `cos theta = cos alpha ` is

`theta = 2npi pm alpha, n inZ`

Therefore, required general solution is

`x = 2npi pm (pi)/(3), n in Z`