Answer
The length of the curve is given by:
$L\approx 8.0091$
Work Step by Step
The curve with polar equation
$$
r=\sin(6 \sin \theta)
$$
is completely traced with $0 \leq \theta \leq \pi $, and the length of the curve is given by the following:
$$
\begin{split}
L=& \int_{0}^{\pi } \sqrt{r^{2}+\left(\frac{d r}{d \theta}\right)^{2}} d \theta\\
&=\int_{0}^{\pi } \sqrt{(\sin(6 \sin \theta) )^{2} +(6 \cos(\theta)\cos(6\sin\theta)) ^{2} } d \theta\\
&=\int_{0}^{\pi } \sqrt{(\sin(6 \sin \theta) )^{2} +36 \cos^{2}(\theta)\cos^{2}(6\sin\theta) } d \theta\\
&\approx 8.0091
\end{split}
$$
