Shakespeare and the Bible

As an aside, I’m noticing a lot of themes from Shakespeare were borrowed from Tanach.  David’s feigning madness to avoid the wrath of the Phillistines is mirrored by Hamlet’s feigning madness to avoid the wrath of Claudius.  Likewise Uriah’s being sent to the front lines with sealed orders for conspiracy to commit his own death is mirrored by Hamlet’s being sent to England with sealed orders for his.  The parable of trees choosing a king is sort of mirrored by, "Macbeth shall never vanquished be, until Great Birnam Wood to high Dunsinaine Hill Shall come against him."   (4.1.92-4)  I’m trying to make a connection between Richard III being surrounded and killed with Shaul’s being surrounded by Phillistines and killed on Mount Gilboa.