Find all solutions of the equation in the interval 0 2 sinx3

Find all solutions of the equation in the interval [0, 2).

sin(x+/3)+sin(x-/3)=1

sin ( x + pi/3) + sin ( x - pi / 3) = 1

(sin x * cos pi/3 + cos x * sin pi/3) + (sin x * cos pi/3 - cos x * sin pi/3) = 1

2*sin x * cos pi/3 = 1

2*sin x * 1/2 = 1 [ cos pi/3 = 1/2]

sin x = 1

sin x = sin pi/2 ------------------------------1

x = pi/2

since sin x is +Ve in 2nd quadrant ,so eq 1 may be written as:

sin x = sin ( pi - p1/2) [ sin ( pi - @) = sin @]

sin x = sin pi/2

x = pi/ 2 ----------ans