Cos 14π/3 = cos 2π/3 prove.

This is a fairly simple procedure. First and foremost, let's put these into degrees shall we? Much nicer to work with.

Now we have cos840 = cos120

As you should recall, a complete revolution around the unit circle (the thing that cos sin and the like deal with) is 2pi, or 360 degrees. As such, sin1 = sin 361, as the second one is a complete revolution around, and thus in the same location. 

So we can subtract 360 from either of our degrees and absolutley nothing changes.

As such we can say, cos480=cos120, and then cos120=cos120. Q.E.D.

Now if you were very staunch to stay in radians, you could do the same thing, just substituting 360 degrees for 2pi, or 6pi/3 in this case.

Hope this helps :)