  (1) In the first (and decisive) step they show that two rays with opposite colours cannot be arbitrarily close. They first show that the diagram  Γ1  depicted in Fig. 1 (where for the time being we ignore the colours  specified in the figure) can be constructed, only if  a0 and a9 are separated by an angle  θ  with 0  ≤  θ  ≤  sin−1(1/3)  (Proof).