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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! 📰 Youll Earn Thousands Unlock Your Power As An Official Mpn Microsoft Partner Network Member 6124508 📰 Lordoftherings Characters 2985413 📰 Flight To Taiwan 1349647 📰 Shocking Facts About The King Hippo That Will Blow Your Mind 6860748 📰 Sosoactive Shocked Everyonethis Secret Ingredient Is Changing Skincare Forever 9789429 📰 You Wont Believe How Cut Rope Magic Transforms Every Craft Project Instantly 822747 📰 Bank Of America Reward Points Credit Card 2878768 📰 Film Armie Hammer 526617 📰 Better Canva 5825836 📰 Drury Inn Suites Burlington Burlington Nc 4210539 📰 Pirates Of The Caribbean Order 2959047 📰 5Iquominated Nppes Strategies Protect Your Data Like Never Before With Proven Identity Security Tactics 7252294 📰 Filter Hard Water 1366694 📰 Wait Reread Create 80 Kg Of A New Mixture With 40 Sand But She Is Starting From 80 Kg Of Soil With 45 Sand 6415466 📰 Am Game 4059607