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Home » I Wasn’t Expecting This—Now I’m Heartbroken Over Your Love! - Abbey Badges

I Wasn’t Expecting This—Now I’m Heartbroken Over Your Love! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Sum = (−1 + 0 + 1 + 2 + 3 + 4 + 5 + 6) = 20.

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So possible coordinates: $(0,1,1)$ or $(0,-1,-1)$.
Check distances:
From $(0,1,1)$ to $(0,0,0)$: $\sqrt{0 + 1 + 1} = \sqrt{2}$
To $(1,1,0)$: $\sqrt{1 + 0 + 1} = \sqrt{2}$
To $(1,0,1)$: $\sqrt{1 + 1 + 0} = \sqrt{2}$
All distances match.
Thus, the fourth vertex is $\boxed{(0,1,1)}$.
Question: Find all angles $z \in [0^\circ, 360^\circ]$ that satisfy
2\sin^2 z - 3\sin z + 1 = 0
Let $x = \sin z$. Then:

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