functions being symmetrical about x=pi

I have this question and I'm not sure what to do.

Show that the function in part 1 is symmetrical about x=Pi.
(Let f(a+x)=f(a-x), for all x, and show that a=Pi)

the function in part 1 is... y=2cosec(x/2)-2

cheers

I'm not sure if the following is right.

Let 2csc(a+x/2) -2 = 2csc(a-x/2) -2
=> 2csc(a+x/2) = 2csc(a-x/2).......................cancelling -2's
=> csc(a+x/2) = csc(a-x/2)..........................dividing both sides by 2
=> sin(a+x/2) = sin(a-x/2).............................inverting both sides
=> sin(a/2)cos(x/2) + sin(x/2)cos(a/2) = sin(a/2)cos(x/2) - sin(x/2)cos(a/2)
=> 2sin(x/2)cos(a/2) = 0
=> cos(a/2) = 0..........................................because we want relationship to hold for all x
=> a/2 = pi/2
=> a = pi