x^2-5x+6=(x-2)(x-3)=0
tanα=2
tanβ=3
tan(α+β)=(tanα+tanβ)/[1-tanαtanβ]
=5/(1-6)
=-1
α+β=3π/4
sin(α+β)=√2/2
cos(α+β)=-√2/2
2sin(α+β)²-3sin(α+β)cos(α+β)+cos(α+β)²
=1+3/2+1/2
=3