What is your daily kcal target? It's possible those last 3kg won't budge because your kcals are actually too low and you just need to readjust a bit.
Plus at 167cm and 56kg, I'd have to say that you are pretty much at your right weight.
What you are looking to do is NOT
lose weight but recomp your bod .. or you might just end up "skinny fat".
To do that, you will undoubtedly need to change up your routine and diet first of all.
Up the kcals, maybe reconsider the macro distribution:
- enough protein to gain/preserve muscle as you lose fat (@ 2g per kg LBM or total weight)
- sufficient essential fats each day (min 0.5g-0.8g per kg BW) and
- the rest carbs ...
and fats and carbs may juggle depending on how well you respond to either of these. If you are carb sensistive, reduce down the amount of daily carbs to a level you can tolerate and see some gradual fat loss. If, conversely, you are fat sensitive, keep the fats down to around your minimum requirements or thereabouts and up the carbs.
It is very much an individual thing.
Make sure you do get some carbs around your workout but frankly your muscles do not atrophy if you don't skull a shake or eat within 30seconds of finishing your workout ... the window of opportunity to get some glycogen into your muscles is quite a few hours.
If you do keep carbs low, throw in a higher carb/kcal day every now and then to keep the metabolism guessing. It can help prevent you plateauing as you appear to have done recently.
Make sure you keep up sufficient resistance training and do some HIIT cardio if required ... whatever works for you.
To work out your daily kcals requirements,
for maintenance (ie to keep your weight but recomp) multiply BW(in kg) x 16
Then just adjust up or down by around 10% kcals for fatloss or to grow lbm.
Start there, give it a few weeks, see how you go. If progress is too fast or too slow, adjust up or down accordingly.
This is just summarised blah blah but hopefully helps a bit