The sin of the golden calf is the source of all subsequent sins.
The half-shekel atoned for the sin of the golden calf, as it bought the sacrificial calves to God in the Holy Temple.
Today has our prayer stands in the stead of the sacrifices, therefore it is the half-shekel.
PRAYING / SHECHINA
When we pray we should first pray for the lack in the Shechina, for there is no lack on Earth that is not first in the Shechina.
How can there be a lack in the Shechina?, for the Jewish people are in a relationship with God, and when there is a lack in one partner, it affects the other.
JEW = SHECHINA
Hence when a Jew prays fervently and restores his soul, he restores the soul of the Shechinah.
In fact as in this world we are transforming the animal spirit which has tremendous Force, it subsequently elevates the Divine (soul.)
JEW = GOD
The Maagid taught that a Jew and God are twins like two halves of one face, hence as we Elevate ourselves we elevate God.
As this relates to ourself, when we transform the 10 selfish desires of the animal soul to the 10 selfless desires of God, for example, instead of lust, unconditional love! instead of power, unconditional resolve! Etc., in this way we elevate even our Divine side.
Now we understand how this service rectifies the tremendous sin of the golden calf, for in elevating ourselves, reaching the Infinity of God, where there is no such thing as Sin.
Just as Machatzis Hashekel / the half-shekel, causes the sacrifices throughout the year, which were done through joy and singing; so too our service causes a lifetime of rejoicing.
This is accentuated when we further contemplate how a single moment in this world of Teshuva / turning to God and Good Deeds, is worth infinite moments in heaven.
Currently it is not visible the infinite reaction of Teshuva and Good Deeds, but in the Messianic era, it will be.