We can calculate each of the trigonometric functions separately and then sum their values.

arcsin(-1/2):
Since the value of arcsin(-1/2) lies in the fourth quadrant, we can write -1/2 as the sine of an angle in the fourth quadrant. The sine function is negative in the fourth quadrant, so we can write -1/2 as sin(-π/6). Therefore, arcsin(-1/2) = -π/6.

arccos(-√2/2):
Since the value of arccos(-√2/2) lies in the second quadrant, we can write -√2/2 as the cosine of an angle in the second quadrant. The cosine function is negative in the second quadrant, so we can write -√2/2 as cos(3π/4). Therefore, arccos(-√2/2) = 3π/4.

arctg(0):
The arctan function, or arctg, is the inverse of the tangent function. The tangent function is zero at 0, so the arctan of 0 will be 0. Therefore, arctg(0) = 0.

Now, summing these values:
arcsin(-1/2) + arccos(-√2/2) + arctg(0)
= (-π/6) + (3π/4) + 0
= 3π/4 - π/6
= (9π - 2π) / 12
= 7π / 12

So, arcsin(-1/2) + arccos(-√2/2) + arctg(0) = 7π / 12.