q-Analog of Pi - Evaluate at q=2, ... ?

[Paul D. Hanna]

SeqFans, 
      The q-analog of Pi is described at: 
http://mathworld.wolfram.com/q-Pi.html 
which gives an iterative algorithm for computing q-Pi 
but the algorithm involves q^2-Pi and q^4-Pi and so 
seems difficult (to me) to find a starting point. 
 
But perhaps one of you can make sense of it, 
or find another way to attain the value, 
such as using the q-sine definition. 
 
Can someone compute q-Pi for q=2, 3, 4? 
 
Of course, q-Pi at q=1 is the classical value 3.14159265...

Thanks, 
     Paul