How to simplify this trignometric expression: $4( 3 \sin \theta)( 3 \cos \theta)$?

Question

I was given a circle with a radius of $3$ and in it was a rectangle and an angle $\theta$ extending from the $x$ axis to up with coordinates of $(3 \cos \theta, 3 \sin \theta)$ and the question asks me to show that the area of the triangle represented by $A$ is equal to $18 \sin 2 \theta$. I figured that the the rectangle has $8$ triangles so using the angle and the coordinates I would find the area of one triangle and multiple it by $8$. So I ended up with $$(8)(.5) b h= (8)(.5)(3 \cos \theta) (3 \sin\theta) = 4( 3 \sin \theta)( 3 \cos \theta).$$ How do you represent this as $18 \sin 2 \theta$?

Thanks and sorry for the question being too long.

Answer 1

$\text{Area}= \frac 1 2 3\sin\theta 3\cos\theta$

Use $\sin\theta \cos\theta = \frac 1 2\sin 2\theta$

$=\frac 9 4 \sin 2\theta$

Multiply by $8$ to get $18\sin 2\theta$

Answer 2

Rather than referring to the area, use the trig identity $\sin(2\theta)=2\sin(\theta)\cos(\theta)$ to write \begin{equation*} 4(3\sin(\theta))(3\cos(\theta)) \\ =36\sin(\theta)\cos(\theta) \\ =18\cdot 2 \sin(\theta)\cos(\theta) \\ =18\sin(2\theta) \end{equation*} hence the result. I am not sure how it could be done with this trig identity.