Point to note here is that you can not jump to 2nd and third talaq until and unless first talaq is complete. One Talaq is a well defined and elaborated procedure in quran. It is not complete without completion of iddat.
It is clearly written in quran that once the first talaq is announced then the period of iddat starts. Iddat is not an optional part of talaq for husband and wife who have lived together. Anyone who believes in book of allah can not deny that.
Until the time period of iddat is not completed, the First talaq is still in progress.
Procedure of 2nd Talaq can initiate when the procedure of first talaq has been completed.
If you or any other member(s) feel that well defined periods of iddat in holy quran are optional part of talaq and can be skipped at will then say it here. and educate us with quranic reference. Thanks
Standard Ahulsunnah belief is slightly different.
All Muslims(sunni,shia,etc) are humans and prone to errors/mistakes. Correction of mistake(s) / error(s) is part of my belief. I have learned this from Hazrat Umar