To solve this expression, let's first simplify the values inside the inverse trigonometric functions:

arccotangent(-√3/3) simplifies to arccotangent(-1/√3), which is equivalent to π + arctan(1/√3) due to the co-function identity of cotangent and tangent.

arccosine(√2/2) simplifies to π/4.

Now, substitute these simplified values back into the expression:

π + arctan(1/√3) + 1/2 * π/4
= π + arctan(1/√3) + π/8
= π + arctan(1/√3) + π/8

So, the simplified expression is π + arctan(1/√3) + π/8.