( 1)

sin 20 cos 100-cos 170 sin 70

= sin 20 cos(90+ 10)-cos( 180- 10)sin(90-20)

=-sin 20 cos 10+cos 10 sin 20

= 0

(2)tan(α+ quartile) =3 to find α.

That is, [tan α+tan (π/4)]/[1-tan α tan (π/4)] = 3.

That is, (tan α+1)/(1-tan α) = 3.

∴ tanα+ 1=3-3tanα

∴ 4tanα=2

∴ tanα= 1/2

∴αis not a special angle.

∴α= kπ+ arctangent (1/2), k∈Z