Let's simplify the expression first:

Given: arcsin (√2/2) + 2arctan(1)

First, find the value of arcsin (√2/2):
This means finding an angle whose sine is √2/2. This angle is pi/4 (45 degrees), since sin(pi/4) = √2/2.

Now, find the value of arctan(1):
This means finding an angle whose tangent is 1. This angle is pi/4 (45 degrees) since tan(pi/4) = 1.

Rewriting the expression with these values:
arcsin(√2/2) = pi/4
arctan(1) = pi/4

Therefore, the expression simplifies to:
pi/4 + 2 * pi/4
= pi/4 + pi/2
= 3pi/4

Thus, the expression sin(arcsin(√2/2) + 2arctan(1)) simplifies to sin(3pi/4).

The sine of 3pi/4 is -√2/2.