To solve this expression, we need to first simplify the inside part of the arcsine function.

Let's start by finding the arcsine of -√3/2:

arcsin(-√3/2) = -π/3

Next, we need to find the negative of this value:

-arcsin(-√3/2) = -(-π/3) = π/3

Now, we can find the arcsine of π/3:

arcsin(π/3) = 60° or π/3

Therefore, Tg(2009arcsin(-arcsin(- √3/2)) = Tg(2009(π/3)) = Tg(669π)

Since the tangent function repeats every π, Tg(669π) is equivalent to Tg(π), and the tangent of π is equal to 0.

So, Tg(2009arcsin(-arcsin(- √3/2)) = 0.