For `n in Z ,` the general solution of `(sqrt(3)-1)sintheta+(sqrt(3)+1)costheta=2i s(n in Z)` `theta=2npi+-pi/4+pi/(12)` `theta=npi+(-1)^npi/4+pi/(12)` `theta=2npi+-pi/4` `theta=npi+(-1)^npi/4-pi/(12)`

Explanation

`(sqrt3-1)sintheta+(sqrt3+1)costheta=2`

`((sqrt3-1)/(2sqrt2))sintheta+((sqrt3+1)/(2sqrt2))costhe
ta=2/(2sqrt2`

`sinpi/12sintheta+cospi/12costheta=cospi/7`

`cos(theta-pi/7)=cospi/4`

`theta-pi/2=2npipmpi/4`

`theta=2npipmpi/4+pi/12`.