To solve this expression, we can use the trigonometric identities:

sin(180 - θ) = sinθ
cos(180 - θ) = -cosθ

Using these identities, we can rewrite the expression as:

sin70 + 2sin110 + 3cos26 - 3cos(180 - 26) + 2cos160

= sin70 + 2sin110 + 3cos26 + 3cos26 + 2cos160

= sin70 + 2sin110 + 6cos26 + 2cos160

Now, we can use the values of sin and cos for the given angles:

sin70 ≈ 0.9397
sin110 ≈ 0.9397
cos26 ≈ 0.8944
cos160 ≈ -0.9397

Plugging in these values, we get:

0.9397 + 2(0.9397) + 6(0.8944) + 2(-0.9397)

= 0.9397 + 1.8794 + 5.3664 - 1.8794

= 6.3061

Therefore, sin70 + 2sin110 + 3cos26 - 3cos154 + 2cos160 ≈ 6.3061.