I would suggest just using the tablets or advice as above. Save weight and forget the brita (you’ll get more in the bottle without it too). As far as I am aware Brita filters will not be effective at removing any pathogens present.
Just did a google and got this from the FAQ –
The content of the original BRITA cartridge is an experienced mixture of ion exchange resin and activated carbon, which is particularly suitable for this type of drinking water conditioning.
The ion exchange resin will remove the hardness, and the carbon the taste.
EDIT – after getting into an argument about this sort of thing before – the MCofS advice seems to be the ideal pragmatic approach.
Have a good trip