Solution:

(cosθ − sinθ)/(cosθ+sinθ) = (1−√3)/(1+√3)

Dividing the numerator and denominator of LHS by cosθ, we get

1 − tanθ/(1+tanθ) = 1−√3 /(1+√3)

Which on simplification (or comparison) gives tanθ = √3

Or θ= 60°