It seems an easy question but I just can find out how I'm supposed to do it: what frequency is needed so that Vin and Vout have a 90° phase shift.
In general, you'll need write down an equation for the output voltage of your circuit, and then find the phase of that in relation to your input. There's no single way of doing that – it depends on the circuit.
For example, the circuit you've posted doesn't have that property – a fixed frequency at which the output has 90° shift relative to its input, since it has positive feedback only, and both for low and for high frequencies is pretty much instable.
It depends if you can tolerate 90 deg or close to that as the ratio of impedances for 2pif*L/R determine how far below the ratio of 1 when the magnitudes are equal where you get 45 deg.
Reusing a nomograph from my other answers for RLCFZ variables, let’s choose an example where all R=1k and all L = 100uH. The breakpoint for this value is ~2MHz, thus 1 decade down in frequency the current will be close to 90 deg at 200kHz and closer below this.
You can slide the signal frequency here and watch the circle slant go from a 90 deg circle above 200kHz towards 2MHz . The scope can be resized and maximized with mouse.