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General laws applicable on fast days:
Rinsing the mouth:  On a public fast day one does not rinse his mouth in the morning. [If however this is causing one discomfort he may be lenient to rinse his mouth.]
May one brush ones teeth on a fast day?
If not doing so will cause one pain or discomfort it is allowed.
May one use mouthwash if lack of doing so will cause pain and discomfort?
Yes it may be used in such a case.
May one bathe on Taanis Esther?
Yes. One may do so even if he is stringent to avoid bathing on the other four fasts.
May one listen to music and dance on Taanis Esther?
 Michaber 567/3; Sefer Haminhagim p. 4 [English]; Ketzos Hashulchan 2 footnote 25 in name of Ateres Zikeinim
 M”B 567/11
 So rules Minchas Yitzchak, based on 567/3 M”B 11 which allows to rinse ones mouth in a case of pain
 Kinyan Torah 2/49; See Mateh Efraim 602/3; Piskeiy Teshuvos 567 footnote 3
 Based on Bach brought in M”B 550/6 that a Baal Nefesh is to be stringent to follow all the oppressions of Tishe Beav on all the other fasts as well. Nevertheless this refers only to the four fasts of scripture which are due to the destruction of the Temple. However on Taanis Esther according to all it is allowed. [Nitei Gavriel 87/18]
 Piskeiy Teshuvos 686 footnote 6