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$$ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}{1+\frac{e^{-6\pi}}{1+\frac{e^{-8\pi}} {1+\ldots} } } } $$
