Advanced Trigonometry, SMB-040 Identify all \(\theta\) values between \(0^{\circ} \leq \theta \leq 360^{\circ}\), such that \(\tan^{2}\theta=\dfrac{1}{3} \) (2 marks) --- 5 WORK AREA LINES (style=lined) --- Show Answers Only \(\theta=30^{\circ}, 150^{\circ}, 210^{\circ}, 330^{\circ}\) Show Worked Solution \(\tan^{2}\theta\) \(=\dfrac{1}{3} \) \(\tan\,\theta\) \(=\pm \dfrac{1}{\sqrt{3}} \) \(\text{Reference angle:}\ \ \tan\,\theta=\dfrac{1}{\sqrt{3}}\ \ \Rightarrow \ \ \theta = 30^{\circ}\) \(\text{Angles exist in all quadrants:}\) \(\theta\) \(=30^{\circ}, (180-30)^{\circ},(180+30)^{\circ},(360-30)^{\circ}\) \(=30^{\circ}, 150^{\circ}, 210^{\circ}, 330^{\circ}\)