To find the value of arccot(-1) + arctan(-1), we can first find the values of each individual term and then add them together.

arccot(-1) is the angle whose cotangent is -1. Since the cotangent function is the reciprocal of the tangent function, we can rewrite this as arctan(-1). The value of arctan(-1) is -π/4.

arctan(-1) is the angle whose tangent is -1, which occurs in the fourth quadrant. The reference angle in the first quadrant is π/4, so the angle in the fourth quadrant is 3π/4. Therefore, arctan(-1) = 3π/4.

Now we can add the two values together:

-π/4 + 3π/4 = 2π/4 = π/2

Therefore, arccot(-1) + arctan(-1) is equal to π/2.