Tango to mimic Diet Coke, regularly finding means of copying pop (4,4)
I believe the answer is:
tape deck
'means of copying pop' is the definition.
(a tape deck might be used to copy pop music)
'tango to mimic diet coke regularly' is the wordplay.
'tango' becomes 'T' (phonetic alphabet: alpha, bravo, charlie etc.).
'to mimic' becomes 'ape' (ape can mean to imitate).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'diet'+'coke'='dietcoke'
The alternate letters of 'dietcoke' are 'deck'.
't'+'ape'+'deck'='TAPE DECK'
'finding' is the link.
(Other definitions for tape deck that I've seen before include "Recorder" , "Drive" , "Hi-fi recording unit" , "Outmoded recording machine" .)