What is the common ratio of the given series:

There isn't one

sin2x / sin x     =  [ 2sinxcosx ] /  sinx  =    2cos x

But

sin3x / sin2x  =  [ -4sin³ x  + 3sin x ]  / [ 2sinx cosx ]  =  -2sin²x/ cosx + [ (3/2)/cosx]  =

[cos2x - 1 + (3/2)] secx  =   [cos2x + 1/2] secx

So.......there is no constant ratio between successive terms as required in a GP