Answer
$A$ = $\frac{\pi}{12}$
Work Step by Step
$A$ = $\int_{-\frac{\pi}{6}}^{\frac{\pi}{6}}\int_0^{\cos3θ}rdrdθ$
$A$ = $2\int_{0}^{\frac{\pi}{6}}\int_0^{\cos3θ}rdrdθ$
$A$ = $\int_{0}^{\frac{\pi}{6}}[r^2]_0^{\cos3θ}dθ$
$A$ = $\int_{0}^{\frac{\pi}{6}}[\cos^2{3θ}]dθ$
$A$ = $\frac{1}{2}\int_{0}^{\frac{\pi}{6}}[1+\cos6θ]dθ$
$A$ = $\frac{1}{2}[θ+\frac{1}{6}\sin 6θ]_{0}^{\frac{\pi}{6}}$
$A$ = $\frac{1}{2}[\frac{\pi}{6}+\frac{1}{6}\sin{\pi}]$
$A$ = $\frac{\pi}{12}$
