Step 1: Read the sentence.
The sentence is 'Let's have a cup of coffee to take a break, ____?' We must add the correct question tag.
Step 2: Note the sentence type.
The sentence begins with 'Let's', which is short for 'Let us'. This makes it a suggestion or an invitation.
Step 3: Recall the special rule.
For any sentence that starts with 'Let's', the fixed question tag is always 'shall we'. This is a set grammar rule.
Step 4: Test the options.
'Can we', 'can't we', and 'shan't we' do not follow the rule for 'Let's'. They sound wrong with a suggestion. Only 'shall we' fits.
Step 5: Place the right tag.
The full sentence becomes 'Let's have a cup of coffee to take a break, shall we?' which is correct and natural.
Step 6: State the conclusion.
The correct question tag is 'shall we'.
\[ \boxed{\text{shall we}} \]