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If ^{cos(theta) - sin(theta)}/ _{cos(theta) + sin(theta)}= ^{1 - (root)3} / _{1 + (root)3}

Find (theta)

$\frac{\cos θ - \sin θ}{\cos θ + \sin θ} = \frac{1 - \sqrt{3}}{1 + \sqrt{3}} \Rightarrow (1 + \sqrt{3}) (\cos θ - \sin θ) = (1 - \sqrt{3}) (\cos θ + \sin θ) \Rightarrow \cos θ - \sin θ + \sqrt{3} \cos θ - \sqrt{3} \sin θ = \cos θ + \sin θ - \sqrt{3} \cos θ - \sqrt{3} \sin θ \Rightarrow - \sin θ + \sqrt{3} \cos θ = \sin θ - \sqrt{3} \cos θ \Rightarrow 2 \sqrt{3} \cos θ = 2 \sin θ \Rightarrow \sqrt{3} \cos θ = \sin θ \Rightarrow \sqrt{3} = \frac{\sin θ}{\cos θ} \Rightarrow \sqrt{3} = \tan θ \Rightarrow \tan θ = \sqrt{3} = \tan 60^{0} \Rightarrow θ = 60^{0}$

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