Well this may be against all the other advise on here, but you can take Valium and zopiclone together as I am prescribed both. Obviously I don't take huge doses but I have taken 0.5mgs of lorazepam and 7.5mgs of zopilcone together when I have been really anxious.
However if you are new to zopiclone I would advise to take it sparingly. I am after 14 yrs taking it, now dependent on it for sleep. Long term use comes with its own problems which the worst one being anxiety in the day. So its a catch 22 with long term use.
BUT I would say to anyone just at the start of medication use ( and this is just my personal experience) if you can find a good AD that suits you then try not to use any if the "addictive" drugs for too long e.g. Zopiclone and Valium. Use these drugs sparingly, when you absolutely have to.

Sarah