The clues aren't expected to mention one another; the theme is all.
Anybody familiar with Macbeth knows about the foretelling:
"Be lion-mettled, proud; and take no care
Who chafes, who frets, or where conspirers are:
Macbeth shall never vanquish'd be until
Great Birnam wood to high Dunsinane hill
Shall come against him."
But then of course:
Messenger: Gracious my lord,
I should report that which I say I saw,
But know not how to do it.
Macbeth: Well, say, sir.
Messenger: As I did stand my watch upon the hill,
I look'd toward Birnam, and anon, methought,
The wood began to move.
Macbeth: Liar and slave!
Messenger: Let me endure your wrath, if't be not so:
Within this three mile may you see it coming;
I say, a moving grove.
Macbeth: If thou speak'st false,
Upon the next tree shalt thou hang alive,
Till famine cling thee: if thy speech be sooth,
I care not if thou dost for me as much.
I pull in resolution, and begin
To doubt the equivocation of the fiend
That lies like truth: 'Fear not, till Birnam wood
Do come to Dunsinane:' and now a wood
Comes toward Dunsinane. Arm, arm, and out!
Oo-er, missus.