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📰 We seek the number of solutions to $ \left| \sin(3\theta) + \cos(4\theta) \right| = 1 $ in $ \theta \in [0, 7\pi) $, then map back to $ t $. 📰 The function $ \sin(3\theta) + \cos(4\theta) $ is smooth and periodic. Its derivative is $ 3\cos(3\theta) - 4\sin(4\theta) $, which is non-zero almost everywhere, implying the function is strictly increasing or decreasing in intervals, but due to high frequency, we estimate number of times it crosses $ \pm1 $. 📰 Instead, count the number of times $ \left| \sin(3\theta) + \cos(4\theta) \right| = 1 $, i.e., when $ \sin(3\theta) + \cos(4\theta) = \pm1 $. 📰 Hotel I Roma 66404 📰 Hayden Hopkins 1871251 📰 Discover The Secret To Earning Extra Income With Covered Callsdont Miss This Proven Strategy 5863795 📰 This Simple Snack Holds The Power To Transform Your Life 1938783 📰 What Are The Differences Between Laptops And Chromebooks 2894857 📰 Is Diablo Iv The Best Expansion Ever Heres Proof You Need To Play Now 2054823 📰 The Coat Guy Reveals The Shocking Secret Behind His Must Have Winter Layering Trick 2549454 📰 Bibury Cotswold England The Hidden Gem Thats Taking Over Instagram Isnt It Stunning 4313362 📰 Why These Hidden Mountain Views Are Worth The Price You Pay 5022985 📰 The One Minute Manager 1139439 📰 Rejecting Belly Button Ring 4465431 📰 Genetic Diversity Definition 4994375 📰 401K Fidelity Sign In Youre About To Unlock Money You Never Knew You Had Tap Now 4029121 📰 Hotel Grand Esmeralda 8617498 📰 Kelly Clarkson Show 2064457