Sine of Multiple of Pi by 2 plus i by Natural Logarithm of Golden Mean

Theorem
Let $z = \dfrac \pi 2 + i \ln \phi$.

Then:
 * $\dfrac {\sin n z} {\sin z} = i^{1 - n} F_n$

where:
 * $\phi$ denotes the golden mean
 * $F_n$ denotes the $n$th Fibonacci number.