Relationship between sine, imaginary number, logarithm, and the golden ratio

Theorem

The following formula holds: $$2\sin(i \log(\varphi))=i,$$ where $\sin$ denotes the sine function, $i$ denotes the imaginary number, $\log$ denotes the logarithm, and $\varphi$ denotes the golden ratio.

References

"Imaginary gold" by John D. Cook
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