Please show step by step that way I can study from this Than

Please show step by step that way I can study from this. Thank you!

Find all solutions exactly:

2 sin(x) + 1 = 0 where 0 x< 2

Solution

2 sin x + 1=0

2 sin x =-1

sin x =-1/2

we know that sin x =1/2 at x= 30⁰ i.e. pi /6

and ,also the value gets negated after every 180⁰ so 180⁰ =pi

so value of sin x becomes -1/2 at pi/6 + pi =7pi / 6

so x = 7 pi / 6 i.e 210⁰