Solve that following equations : `(sqrt(3)-1)costheta+(sqrt(3)+1)s intheta=2`

Explanation

Given:
`(sqrt3+1)costheta+(sqrt3-1)sintheta=2`
Let `(sqrt3+1)=rcosalpha`
`(sqrt3-1)=rsinalpha`
`rcosalphacostheta+rsinalphasintheta=2`
`r(cosalphacostheta+sinalphasintheta)=2`
`r(cos(theta-alpha))=2`
`cos(theta-alpha)=2/r`
`implies cos(theta-alpha)=1/sqrt2`
`implies cos pi/4`
`r=(sqrt((sqrt3-1)^2+(sqrt3+1)^2`
`=sqrt8`
`=2sqrt2`
`tanalpha=(sqrt3-1)/(sqrt3+1)`
`implies tan (pi/3-pi/4)`
`implies alpha=pi/12`
`(theta-alpha)=2npi pm pi/4`
`alpha=pi/12`
`theta=2npi pm pi/4 pm pi/12`