"a complete coincidence" is correct and usable in written English. You can use it when two or more unrelated events happen at the same time, without any apparent cause. For example: "It was a complete coincidence that we both happened to be at the same restaurant at the same time.".
"That was a complete coincidence," said Mikey.
It's a complete coincidence, albeit a quite bizarre one".
Or is this just an attempt to make an issue out of a complete coincidence?
I didn't know it was part of Goodison Park – a complete coincidence.
Statistical evaluation of the results of all three methods revealed an almost complete coincidence in the results of BAL and TBS with the lower threshold (10 CFU/ml).
I never know, and that's what excites me -- when the work is almost the result of a happy accident, or complete coincidence".
Mobiquity took down the l page in late July as part of an ongoing site redesign – complete coincidence, not conspiracy.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union