Vtyjkyuk

I have to determine the first order probability density function for $w(t, epsilon)$, with the hypothesis that I have two statistically independent functions $x(t, epsilon)$ and $y(t, epsilon)$ uniformly distributed in $[-frac12,frac12]$.

$$
w(t,epsilon) = z^2(t,epsilon)
quadtextandquad
z^2(t,epsilon) = (x(t,epsilon)+y(t,epsilon))^2
$$

I set a $t$ for the evalutation, and $epsilon$ is given, so my functions become random variable, defined this way:
$$
W = Z^2 = (X+Y)^2
$$

For any variable I have a probability density like:
$p_x(x)$ for $x(t,epsilon)$

So I can define that
$p_z(z) = p_x(x) cdot p_y(y)$.

Having $p_x(x) = operatornamerect(x)$ and $p_y(y) = operatornamerect(y)$, then $p_z(z) = operatornametri(z)$.

By having triangle as a result for $z$, I have to consider the $p_w(w)$ in two parts $(-infty, 0)$ and $(0, +infty)$, so in first part I got
begingather*
p_z(z) = (1+z)
cdot
operatornamerectleft( z + frac12 right), \
z_1 = -sqrtw, \
p_z(z_1) = (1 - sqrtw)
cdot
operatornamerectleft( w - frac12 right).
endgather*
With this assumptions, how can I say that:
$$
operatornamerectleft( frac12 - sqrtw right)
= operatornamerectleft( w - frac12 right)
$$

Please, help me, I'm really going crazy.

Edit:
$operatornamerect$ is the rectangular function.