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📰 We are told this maximum is $ \sin \theta $ for $ 0 < \theta < \pi $. 📰 \sin \theta = \frac{\sqrt{2}}{2} \quad \Rightarrow \quad \theta = \frac{\pi}{4} \quad \text{or} \quad \theta = \frac{3\pi}{4} 📰 Both are in $ (0, \pi) $, but since the maximum imaginary part is positive and corresponds to $ \frac{\sqrt{2}}{2} $, and the angle is often taken as the acute one in such contexts, but the problem asks for $ \theta $ such that $ \sin \theta = \text{max imag part} $, and $ \theta $ is to be found. However, $ \frac{\sqrt{2}}{2} = \sin \frac{\pi}{4} = \sin \frac{3\pi}{4} $, but $ \frac{3\pi}{4} $ is larger and still in range. But since the root has argument $ \frac{3\pi}{4} $, and the imaginary part is $ \sin \frac{3\pi}{4} = \frac{\sqrt{2}}{2} $, the value $ \theta $ such that $ \sin \theta = \frac{\sqrt{2}}{2} $ and corresponds to the phase is naturally $ \frac{\pi}{4} $, but the problem says "expressed as $ \sin \theta $", and to find $ \theta $. However, since $ \sin \theta = \frac{\sqrt{2}}{2} $, 📰 Treme Hbo 4930623 📰 Why Every Tech Enthusiast Must Watch Jason Schreiers Latest Insider Interview 4049745 📰 How To Link Fortnite Accounts 1734839 📰 Cramming 506607 📰 Where To Watch Iowa Hawkeyes Football Vs Wisconsin Badgers Football 2057972 📰 Share Price Whirlpool 7255683 📰 Davis Librarys Most Shocking Discovery Will Change Everything You Thought You Knew 7516759 📰 Saint Petersburg Russia 2607708 📰 Dubai And Hotels 4837184 📰 Ghost Rider Enemies 3258378 📰 You Wont Believe How Easy Like Never Before Make Your Bracket Break The Internet 6125795 📰 Savage Daughter 726741 📰 Ghanouj 8207511 📰 Kingdom Hearts 1 Bright Crystal 2575495 📰 This Saint Berduoodle Just Went Viral Is It The Cutest Dog Youll Ever See 6657846