How much of the Greece's public debt is created by its trade deficit?
As an accounting identity, it is required that the current account surplus (deficit) +  capital account surplus (deficit) = 0. This is known as the balance of payments (BOP) identity . So if Greeks are importing more Euros worth of goods and services than they are exporting it must be that, consolidating across those outside of Greece, non-Greeks are buying more Euros worth of Greek assets than they are selling. 

However, this accounting identity says nothing about who in Greece is selling and who outside of Greece is buying. It need not be that the government is involved at all. If the Greek government borrows more than before the household sector might offset this greater borrowing more than one for one with greater savings (BOP decreases), exactly offset (no change in BOP), partially offset it (change in balance of payments less than increase in government spending), or also borrow (increases in BOP more than change in government spending).