Explanation:

- The given equation is \(\sin \theta + \cos \theta = \sqrt{3} \cos(90 - \theta)\).

- Using \(\cos(90 - \theta) = \sin \theta\), substitute it in the equation: \(\sin \theta + \cos \theta = \sqrt{3} \sin \theta\).

- Simplify to get: \(\cos \theta = (\sqrt{3} - 1) \sin \theta\).

- Use the identity \(\tan \theta = \frac{\sin \theta}{\cos \theta}\).

- Therefore, \(\tan \theta = \frac{1}{\sqrt{3} - 1}\).

- Simplify the expression: Multiply numerator and denominator by \(\sqrt{3} + 1\) to get \(\tan \theta = \frac{\sqrt{3} + 1}{2}\).

- Option 3: (\(\sqrt{3} + 1\))/2 is the correct answer.