a^2+a+1=0
(a-1)(a^2+a+1)=a^3-1=0
a^3=1
a^1000+a^2001-a^3002
=a^(3*333+1)+a^(3*667)-a^(3*1000+2)
=a+1-a^2
=a+1-a^2-a-1 +a+1
=2a+2
=-2a²