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. \(27^\circ\), \(3^{rd}\) quadrant, \(360^\circ < \theta < 720^\circ\)
2. \(\frac{5}{13}\pi\), \(4^{th}\) quadrant, \(-2\pi < \theta < 0\)