Should I use:
This picture was taken for the very first time.
or:
This picture was taken for a very first time.
This picture was taken for the very first time.
This above is correct because 'the' refers to the one instance of that picture being taken, which is factually correct.
If 'a' were used instead of 'the' then it would indicate that this particular picture was being taken more than once with the sentence referring to only one of those instances. This is wrong because it's not possible to take a particular photograph more than once (although it is possible to take multiple photographs of the same scene).