Single supply op amp to convert 0-5VDC to +/-2VDC (microcontroller to line level)
I think you are trying to make sure that your output signal does not have a DC offset with a peak voltage of 2 V. Simply you can remove a DC offset by inserting a series capacitance:







simulate this circuit &ndash; Schematic created using CircuitLab

Which will produce the following conversion:



But will be a high pass so you must choose your capacitance values to ensure that you don't reduce the amplitude of the sine at the spec'd frequency (which you haven't supplied).



Another further improvement would be to place an op-amp buffer after this, however that would require a dual supply (i.e. ±V).

The important equation for your amplitude is from the resistor divider:

$$
V_\mathrm{out} = V_\mathrm{in}\frac{R_2}{R_1 + R_2},\quad 4 = 5 \frac{40}{10 + 40}
$$