How do you find all solutions for 5sinθ+3=3?

With #! i’ve tried to figure it out but i can’t.

Galen sold tickets of his church’s carnival for a total of $2,820. children’s tickets cost $3 each and adult tickets cost $5 each. the number of children’s tickets sold was 30 more than 3 times the number of adult tickets slod. how many children’s ticket and how many adult tickets did he sell?

Answer for 10 points show work you guys in advanced < 3