Relationship between arcsin and arccsc

Theorem: The following formula holds: $$\mathrm{arcsin}(z) = \mathrm{arccsc}\left( \dfrac{1}{z} \right),$$ where $\mathrm{arcsin}$ denotes the inverse sine function and $\mathrm{arccsc}$ denotes the inverse cosecant function.

Proof: █