# All Roots

Algebra Level pending

$\large \sinh(z)=i$

The roots of the equation can be expressed as $$\displaystyle z = i \left(an + \frac{b}{c} \right)d$$ , where $$n$$ belongs to set of integers and $$i = \sqrt{-1}$$ with $$a,b,c,d$$ are real constants with $$b , c$$ as co-primes.

Evaluate $$\large \frac{abcd}\pi$$.

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