\[\large \sinh(z)=i \]

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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