To simplify this expression, we will need to use trigonometric identities and properties.

Let's break down the expression step by step:

arc cos(-√2/2) = 3π/4 (this is the angle whose cosine is -√2/2 in the fourth quadrant)arc cos(1) = 0 (cosine of 1 is 0)2arc sin(1/2) = 2*(π/6) = π/3 (sine of π/6 is 1/2)arc tan(√3/3) = π/6 (tangent of π/6 is √3/3)

Now we substitute these values back into the expression and simplify:

4(3π/4) - 3(0) + 2(π/3) - π/6

= 12π/4 - π/2 + 2π/3 - π/6
= 3π - π/2 + 2π/3 - π/6
= 6π/2 - π/2 + 4π/6 - π/6
= (12π - 3π + 8π - π)/6
= 16π/6
= 8π/3

Therefore, the simplified expression is 8π/3.