In Tobira chapter 11 grammar, one of the examples is
奈良は京都と並んで、古い歴史のある町で、日本の首都だったこともある。

I don't seem to find any information about たこともある on the entire web.

I understand there is no difference between (verb casual non
past)+こともある/ことがある, which means sometimes or there are times when.

I was warned not to confuse with the construction (verb た-form)+ことがある, which
means to have done something before. Is たことがある the same as た+こともある?
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grammar usage particles phrases particle-も
How to analyze たこともある?
I think you should stick just to ことがある. (In this sense, yes たことがある is
た＋ことがある).

ことがある means _did something before_ as you understand. More abstractly, it
expresses a past experience.

  * 私はアメリカに行ったことがある I've been to the US.

Whether it translates to present perfect or past tense in English depends on
the meaning.

  * 奈良は日本の首都だったことがある

can be translated _Nara **was once** the capital of Japan_. Here it in a sense
express an 'experience' of the city Nara.

こともある could be _Nara was also ..._ , but it should be clearer to say _There
was also a time when Nara was the capital of Japan_.
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Short answer: であることがある becomes だったことがある by adding た to the main verb.(†) It
then comes だったこともある by replacing が with も to mean "additionally/also".

In this case も/が both work, and doesn't change the meaning of the sentence too
much. You can replace が with も when mentioning _one more thing_. It can add
emphasis, like "guess what, it was also..." but the emphasis is usually weak,
if any (and that is why I say it doesn't change the meaning too much). If you
start the paragraph by using Xも (which implies there is something similar to X
in the immediate context), that would probably be strange, but that's not the
case here.

If you want to more clearly emphasize the last part, you can say
日本の首都だったことさえある.

This is independent from the たことがある construction. The same distinction applies
to its non-past form: すること **が** ある ("sometimes I do X"), すること **も** ある
("sometimes I also do X") and すること **さえ** ある ("sometimes, I even do X"). Or
any other cases like 花 **が** 咲いてます / 花 **も** 咲いてます / 花 **さえ** 咲いてます.

(†) Technically, there is one more step in between (である→であった→だった) but I think
that's besides the point here.
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answer