Given: \[ \tan(θ + 15^\circ) = \sqrt{3} \Rightarrow \tan(θ + 15^\circ) = \tan 60^\circ \Rightarrow θ + 15^\circ = 60^\circ \Rightarrow θ = 45^\circ \] \[ \therefore \sin θ + \cos θ = \sin 45^\circ + \cos 45^\circ = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \frac{2}{\sqrt{2}} = \sqrt{2} \quad \text{(Answer)} \]