Let's simplify the expression step by step.

First, we know that sin(2π) = 0 and sin(3π) = 0, so:
sin(2π + a) = sin(a)
sin(3π/2 + a) = -sin(a)

Now the expression becomes:
-sin(a) + sin(a) / 2cos(-a)sin(-a) + 1

Next, we know that sin(-a) = -sin(a) and cos(-a) = cos(a), so:
-sin(a) + sin(a) / 2cos(-a)sin(-a) + 1 = -sin(a) + sin(a) / 2cos(a)(-sin(a)) + 1

Now we can simplify further:
-sin(a) + sin(a) / 2cos(a)(-sin(a)) + 1 = -sin(a) - sin(a) / 2cos(a)sin(a) + 1

Finally, we can simplify the expression by consolidating the terms:
-sin(a) - sin(a) / 2cos(a)sin(a) + 1 = -sin(a) - 1/2 + 1
= -sin(a) - 1/2 + 1
= -sin(a) - 1/2 + 2/2
= -sin(a) + 1/2

Therefore, the simplified expression is:
-sin(a) + 1/2