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. \(\alpha = 30^{\circ}\), \(\theta\) is in the \(4^{\text{th}}\) quadrant, \(180^{\circ} < \theta < 540^{\circ}\).
2. \(\alpha = 17^{\circ}\), \(\theta\) is in the \(2^{\text{nd}}\) quadrant, \(-720^{\circ} < \theta < -360^{\circ}\).
3. \(\alpha = \frac{\pi}{4}\), \(\theta\) is in the \(3^{\text{rd}}\) quadrant, \(-2\pi < \theta < 0\).
4. \(\alpha = \frac{2\pi}{5}\), \(\theta\) is in the \(1^{\text{st}}\) quadrant, \(3\pi < \theta < 5\pi\).