Trigonometry - Exact Trigonometric Values and the Unit Circle

Given the basic angle, \(\alpha\), and the quadrant in which \(\theta\) lies, find the value of \(\theta\).

1. \(\alpha = 60^{\circ}\), \(\theta\) is in the \(2^{\text{nd}}\) quadrant, \(-180^{\circ} < \theta < 180^{\circ}\).
2. \(\alpha = 35^{\circ}\), \(\theta\) is in the \(4^{\text{th}}\) quadrant, \(0^{\circ} < \theta < 360^{\circ}\).
3. \(\alpha = \frac{4\pi}{9}\), \(\theta\) is in the \(1^{\text{st}}\) quadrant, \(0 < \theta < 2\pi\).
4. \(\alpha = \frac{3\pi}{7}\), \(\theta\) is in the \(3^{\text{rd}}\) quadrant, \(-4\pi < \theta < -2\pi\).