Verified answer

Use the identities for sin(A + B) and sin(A - B)

sinxcos(pi/3) + sin(pi/3)cosx + sinxcos(pi/3) - sin(pi/3)cosx = 1

--> 2sinxcos(pi/3) = 1

--> sinxcos(pi/3) = 1/2

--> (1/2)sinx = 1/2

--> sinx = 1

on [0, 2pi) this only occurs at pi/2