The exercise description says:

In Exercises 87 - 92, solve the inequality. Express the exact answer in interval notation, restricting your attention to−2PI≤x≤2PI

91. sin(2x) >= sin(x)

The answer is missing one interval (actually one point)

[2PI,2PI]

According to the description 2PI is part of the domain to consider and in this point sin(2x) is equal to sin(x).

So as far as I understand the full answer should be:

[-2PI,-5PI/3]U[-PI,-PI/3]U[0,PI/3]U[PI,5PI/3]U[2PI,2PI]

Of course I could be wrong, or I missed something in this exercise.