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Home / Case 2:** $ 3\theta = 2k\pi - 2\theta $

Case 2:** $ 3\theta = 2k\pi - 2\theta $

February 22, 2026

$Case 2:** $ 3\theta = 2k\pi - 2\theta $$

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Subtract $ 2\theta $ from both sides:
\theta = 2k\pi
Within $ [0, 2\pi) $, the only solution is $ \theta = 0 $.
Add $ 2\theta $ to both sides:
5\theta = 2k\pi \quad \Rightarrow \quad \theta = \frac{2k\pi}{5}
We now find all values of $ k $ such that $ 0 \leq \frac{2k\pi}{5} < 2\pi $.

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