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📰 \boxed{\dfrac{12}{7}}Question: Find all angles $ \theta \in [0^\circ, 360^\circ] $ that satisfy $ 2\cos(2\theta) + 1 = 0 $, inspired by periodic patterns in environmental data trends. 📰 Solution: Start by solving $ 2\cos(2\theta) + 1 = 0 \Rightarrow \cos(2\theta) = -\frac{1}{2} $. The general solutions for $ 2\theta $ are $ 2\theta = 120^\circ + 360^\circ k $ or $ 2\theta = 240^\circ + 360^\circ k $, where $ k \in \mathbb{Z} $. Dividing by 2, $ \theta = 60^\circ + 180^\circ k $ or $ \theta = 120^\circ + 180^\circ k $. For $ \theta \in [0^\circ, 360^\circ] $, the solutions are $ 60^\circ, 120^\circ, 240^\circ, 300^\circ $. 📰 \boxed{60^\circ, 120^\circ, 240^\circ, 300^\circ} 📰 How The 72M Hhs Ocr Hipaa Settlement In November 2025 Is Changing Healthcare Data Rules Forever 621930 📰 Dietary Guidelines For Americans 21690 📰 Subtract The Freed Memory From The Original Usage 3787866 📰 5Todays Game Changer Dow Jones Industrial Shatters Records In Todays Flash Rally 6892813 📰 Skims Thong 2045152 📰 Powerball Pull Time 4960286 📰 Click Here To Learn The One Method That Truncates Sql Tables Like A Pro 4304153 📰 Video Card Game Play Reefed Top Strategies To Dominate Online Now 2703034 📰 Big 5 Stock Analysis Is This The Blockbuster Investment Trend You Need To Know 5113050 📰 Meaning Hindrance 2998293 📰 Mastercraft Tires Exposedthe Only Choice That Keeps You Safe On Every Road 3442985 📰 Tri C Space Unlocks Power Beyond Imaginationyoull Be Stunned 1250437 📰 This Simple Habit Is What Calling Fidelity Actually Relies Ondiscover Why 5684823 📰 Juan Ibarra 979702 📰 Arc Raiders Ps5 3081883