We know that the domain and range of the principal value branch of function sin−1 is defined as:
sin−1 " [- 1 , 1] → [−

π

2

,

π

2

]
∴ sin [

π

3

−sin−1(−

1

2

)] = sin [

π

3

−(−

π

6

)]
= sin [

π

3

+

π

6

]
= sin [

π

2

]
= 1