How to assemble three 60mer nts by pcr?
In order to assemble your TAG oligos by PCR you will need to redesign your primers so they are complementary to the TAG oligos as DNA polymerases work by adding nucleotides to the 3' end of a DNA strand.
Your design would look like this :

Now with this design you won't be able to assemble everything together as TAG-3 complementarity to primer 2 only presents 5' ends to be extended, which your DNA polymerase can't do. So you can either order the entire reverse complement of your TAG-3 oligo or design a primer 3 that would anneal at the 3' end of TAG-3 to amplify TAG-3.
With all these parts, you should be able to assemble everything in a single reaction, but depending on your downstream process you may have to purify the product of interest as the single reaction will generate intermediates (1, 2, 3, 1+2, 2+3).