As the ultimate aim is to generate a three phase waveform, rather than simply shift a sine waveform by 120 degrees, the following circuit may be of use.
The basic idea is to drive a number of time-shifted square waves of the right frequency through a shift register. By summing precise amounts of each square wave, we can eliminate all harmonics except for those at frequencies of the top clock +/- 1.
Some may see it as using too much 'old technology', but it's a very flexible technique, applicable to many more applications than this. Of course if you're already using an MCU, then your 'shift register' outputs could be just a bunch of GPIOs.
For instance, if the clock is 12 x the required output frequency (as the circuit below), it generates the fundamental, and then no harmonics until the 11th, 13th, 23rd, 25th etc. A filter to remove the 11th harmonic can have a very relaxed transition band so can be low order, or in some applications, may not be necessary at all.
The output voltage is very stable, depending as it does on the power supply voltage. The output frequency can be controlled by choosing the top clock frequency.
In the diagram below, the NOT gate round the first six stages of the shift register produces a /12 Johnson counter. This is for a 4018/74HC164 type register where the outputs are delayed only one clock. If you used a HC595 clocking the output register at the same time, the outputs are delayed an extra clock, and the NOT gate has to come from the previous tap.
Starting from a proper RESET, this counter will continue to run correctly. However, it is possible, if some glitch is received, or if the clock/reset timing is not correct, that some illegal states can circulate round the counter. If you want to detect or avoid these, then the input to the shift register could be taken from a /12 counter, or you could use logic to detect illegal sequences and reset the registers.
By choosing where to tap off each output, we can control the relative phases of the multiple outputs. Here the outputs are taken every 4th tap, to give us our three phases.
The resistors are chosen so that their conductance is given by points on a sinewave. For a /12 method it's particularly straightforward, 30 degrees per tap. We therefore have
The resistor accuracy determines the harmonic suppression. For instance you need 1% resistors to give you roughly -40dBc harmonics. It's worth building the 11.55k from a 11k + 560Ω (E24 values).
simulate this circuit – Schematic created using CircuitLab
We can generate the output with ratios other than 12x. For three phase generation, it's convenient to use a ratio with a factor of 3 in it, but even that's not essential. For other ratios, we simply choose the conductance of the summing resistors for the appropriate points on a sine waveform.