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Home » Therefore, the sum is \( \boxed{\sqrt51 - 1} \). - High Altitude Science

Therefore, the sum is \( \boxed{\sqrt51 - 1} \). - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Since $ \phi = 3\theta $, we substitute:

📌 3\theta = 30^\circ + 360^\circ k \quad \Rightarrow \quad \theta = 10^\circ + 120^\circ k

📌 3\theta = 330^\circ + 360^\circ k \quad \Rightarrow \quad \theta = 110^\circ + 120^\circ k

📌 We now find all $ \theta \in [0^\circ, 360^\circ] $ by plugging integer values of $ k $.

📌 For $ \theta = 10^\circ + 120^\circ k $:

📌 $ k = 0 $: $ 10^\circ $

📌 $ k = 1 $: $ 130^\circ $

📌 $ k = 2 $: $ 250^\circ $

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