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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} $, 📰 5 2025 401K Total Surprise Millennials Need To Act Fast Before Its Too Late 1378621 📰 Amer Corporation 9661273 📰 Cake Toppers That Steal The Show Heres How To Elevate Every Dessert Event 6945538 📰 How Much Do Influencers Make 4539191 📰 Cat Scales Close To Me 5681109 📰 Double The Heat Double The Stars Arsenal Fc Vs Crystal Palace Fc Lineup Showdown 4896251 📰 The Shocking Truth Behind Bitni Spirs No Ones Talking Aboutfeel Every Remove 9446333 📰 Shape Your Future Fast With The 1 Earnin Appyou Wont Believe What It Realizes 9044132 📰 Bubble Popping Games 5707177 📰 Watch This Deep Dive Into Why Christian Bale Stole The Spotlight As Batman 920058 📰 Robert Palmer Addicted To Love 7273928 📰 You Wont Guess The Secret Technology Inside Every 2022 Toyota Camry 5362879 📰 Can You Live Without A Gallbladder 1510370 📰 Unveil Her Secret Every Shawl Detail Was Made To Remind You What She Holds Back 7701733 📰 Giants V Bills 7302461