The second argument to unwrap is not the period of the input data, but the tolerance. The function always unwraps data assuming a 2π interval. That is, it wants to see that x(i)-x(i+1) is larger than the tolerance before unwrapping, and smaller after unwrapping. In the case of a tolerance of pi/2, if, for example, x(i)=0 and x(i+1)=3, the jump is larger than the tolerance, but adding or subtracting 2*pi to x(i+1) does not improve things.

One work-around would be to multiply the input by 2, and divide by 2 after unwrapping:

unwrap(theta_atan * 2) / 2

However, it is always best to use atan2 to obtain an angle.

You need to transform the interval (-pi/2, 0) into (pi/2, pi). For that purpose you can use mod:

y = mod(atan(x), pi);

Another possibility: use atan2. This lets you specify the sine and the cosine of the desired angle as separate inputs, and thus you can control the output interval. To obtain an output in (0, pi), the sine (first input of atan2) should be positive. Therefore you can use abs(x) as first input and move the sign of x to the second input:

y = atan2(abs(x), sign(x));

Atan takes single argument and Atan2 takes two arguments.The purpose of using two arguments instead of one is to gather information on the signs of the inputs in order to return the appropriate quadrant of the computed angle, which is not possible for the single-argument Atan

Atan2 result is always between -pi and pi.

Reference: https://en.wikipedia.org/wiki/Atan2