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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! 📰 City Of Fairborn 5568473 📰 Life Kitchen 9566038 📰 The 1 Buddy The Elf Costume Trick To Look Like A Magic Makertry It Today 7938188 📰 What Bluit Did Next Will Make You Explore This Trending Phenomenondont Miss Out 2783613 📰 Slack Download Windows 7487903 📰 Unlock Hidden Data Count Every Non Empty Cell Instantly With Excel Countifs 5309151 📰 Yes Its Easy Craft The Ultimate Chest In Minecraft And Store Lore Level Items 6281671 📰 Two Sisters Bakery 3063306 📰 Carrot Nutrition 8904251 📰 A Box Is Shaped Like A Rectangular Prism With Dimensions 8 Cm By 6 Cm By 4 Cm If The Box Is Filled With Cubes Of Side Length 2 Cm How Many Cubes Can Fit Inside 3343840 📰 Volume Equation 8337949 📰 How To Check My Verizon Internet Speed 3609021 📰 Actress Amy Landecker 456290 📰 Youre Wearing Grey But Somethings Watching Inside 3420538 📰 A Companys Revenue Grows 15 Annually If It Earned 2 Million In 2020 What Was It In 2023 2972436