The first parameter of this problem tells us we're going around our unit circle just once, so we can't have values of x greater than 2π or less than 0π. The given equation can be simplified using these steps:
2cosx -√3 = 0
2cosx = √3
cosx = √3/2
Now we just have to look at our unit circle and figure out which x values equal √3/2. Hopefully you'll notice that cosx = √3/2 at π/6 and 11π/6 (a.k.a. 30º and 330º). You can also plug this into your calculator:
x = cos-1(√3/2). However, you'll only get 1 answer from that - 30° or π/6. Be careful when using calculator simplification.