If $e^{i \theta} = \frac{2 + i \sqrt{5}}{3},$ then find $\sin 4 \theta.$
Question:
If $e^{i \theta} = \frac{2 + i \sqrt{5}}{3},$ then find $\sin 4 \theta.$
Answer:
Let's think step by step.

user
-\frac{8 \sqrt{5}}{81}
If $e^{i \theta} = \frac{2 + i \sqrt{5}}{3},$ then find $\sin 4 \theta.$
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