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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! 📰 How A Single Tone Can Transform Your Moodwithout You Knowing It 2630121 📰 Npni Locator The Revolutionary Tool Hiding Your Location Like Magic 8370668 📰 Drawn Oranges 1861898 📰 Top 10 Fantasy Football Leagues That Dominated The Seasondont Miss This 8871439 📰 How Many People Are In The World In 2025 7869712 📰 Desoto City Hall 6974297 📰 Top Unblocked 3 Player Games You Can Play Free Instantly No Account Required 8893021 📰 Alex P Keaton 3137672 📰 Best Moisturiser For Ageing Skin 806265 📰 1993 World Series 6704106 📰 Best Romance Movies Of All Time 7536799 📰 Where To Watch Tampa Bay Buccaneers Vs Houston Texans 7116286 📰 Waitreread Within The First Quadrant But No Bound So Unless Restricted Infinite But That Contradicts The Format 1545516 📰 Chicken Cheesesteak 46700 📰 Abc The View 5904516