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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! 📰 Who Owns Lowes 8120893 📰 What Does Elizabeth Mean 795684 📰 Ectropion Cervicale 1430162 📰 Jp Morgans Decades Long Hiatus Endsheres How The Bank Will Transform 2873717 📰 Flawless Short Bob Haircuts Youll Want To Recreate At Home 6179363 📰 Verizon Coverage Hawaii 3032480 📰 Lawmakers Silenced The Debate The Truth Behind Texass Thc Ban Takeover 5782526 📰 Airforce 7939406 📰 Nxp Stock Surge Is This The Big Break No Ones Talking About Yet 1875580 📰 Hilton Garden Inn Savannah Historic District 6567394 📰 Wti Stock Twits Spike Overnightexperts Reveal The Hidden Trend Driving Gains 8405786 📰 You Wont Believe How Much Minecraft Really Costsheres The Shocking Total 7467801 📰 Vodka Delivery 3481341 📰 How To Reset A Verizon Modem 9583772 📰 Waterburys Climate Shocks Whats Hiding In The Air 7121956