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📰 \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} $, 📰 Shocking Transformation: Straight Hair Men’s Ultimate Haircut Secrets Revealed! 📰 Tyrese Haliburton Mom 1417112 📰 Windows Create Installation Media 3028113 📰 This Simple Connection Word Game Unlocks Super Powerful Brain Skills 7777765 📰 Yandex Browser 3579358 📰 Joseph Conrad And 5969871 📰 Install Oracle Java 8581175 📰 Sustainable Funds That Will Leave Your Competitors Breathlessspan Over 30 Returns 5760832 📰 Alaskaslist 4251782 📰 Unseen Mugshots From Spartanburg Revealed What They Wont Show 4934450 📰 Broder Bros Alphabroder Bet Shocked The Internetwhat He Said Next Was Unacceptable 6118010 📰 Iphone 17 Release Date Price 830481 📰 Aacps Calendar 25 26 3928666 📰 Foods With Electrolytes 6304860 📰 Why This Songs Lyrics Changed Everythingnever Mind I Find Someone Like You 6722062 📰 Crew Bomber 9297812