Third shekel?

I saw this thing from TYH nation about when in the Book of Nehemiah it calls for Jews to pledge a third of a shekel, which is abnormal as the Tanakh usually asks Jews to pledge half a shekel. They said this had something to do with the Persian siglos, but a Persian siglos is worth a half shekel, so where does the third of a shekel thing link to the siglos? Sigloi weigh about 5.5 grams, which is extremely close to the half-shekel at 5.7 grams. A third of a shekel weighed about 3.4 grams.