Answer:
[tex]12\sin{(2\theta)}\cos{(\theta)}[/tex]
Step-by-step explanation:
The appropriate trig identity is ...
[tex]\sin{a}+\sin{b}=2\sin{\left(\dfrac{a+b}{2}\right)}\cos{\left(\dfrac{a-b}{2}\right)}[/tex]
Here, you have a scale factor of 6 and a=3θ, b=θ. Filling in these values gives ...
[tex]6\sin{3\theta}+6\sin{\theta}=12\sin{\left(\dfrac{3\theta+\theta}{2}\right)}\cos{\left(\dfrac{3\theta-\theta}{2}\right)}\\\\=12\sin{(2\theta)}\cos{(\theta)}[/tex]
