Think complex...

From Euler's Formula , we know that
$\large \sin\theta = \dfrac{ e^{\iota\theta} - e^{{-\iota}{\theta}}}{2\iota}$

$Z = \iota \sin\left(\iota \dfrac{\pi}{6}\right)$

$Z = \dfrac{ e^{\iota\left( \iota\frac{\pi}{6}\right)} - e^{-\iota\left( -\iota\frac{\pi}{6}\right)}}{2}$

$Z = \dfrac{ e^{- \frac{\pi}{6}} - e^{\frac{\pi}{6}}}{2} = -0.548 \ \text{(real number)}$

As we know, the series of sin(x) contains odd powers of $x$ , $\begin{aligned} \sin x &=& x - \dfrac{x^3}{3!} + \dfrac{x^5}{5!} - \dfrac{x^7}{7!} + \cdots \end{aligned}$ ,

So here if we put $x=Ai$ , $A\in R$ then the series will have complex terms $+i$ or $-i$ and on multiplying with $i$ , the series will have $+1$ or $-1$ in place of $i$ everywhere, so it will be completely a real number