Finding angular frequency in electric circuit

[sodper]

Homework Statement

At a certain angular frequency, the phase difference between $$U_{2}$$ and $$U_{1}$$ is $$180^{\circ}$$.
a) Calculate this angular frequency
b) Calculate $$U_{2}$$ at this angular frequency

See the attachment for circuit configuration.

Homework Equations

Ohms law: $$U = Z \cdot I$$
Voltage: $$U = \hat{U} cos(\omega t + \alpha)$$

The Attempt at a Solution

I can't seem to find the relation between phase difference and angular frequency.

I've tried to compute the equivalent double-pole, separating the coil with voltage $$U_2$$ from the rest och the circuit, with the following result:

Idle current:
$$U_t = \frac{\omega^2 L^2 + Rj\omega L}{R^2 + \omega^2 L^2} U_1$$

Equivalent impedance:
$$Z_0 = \frac{\omega^2 RCL - R - j\omega L}{\omega^2 LC - j\omega RC}$$

And from this I've calculated $$U_{2}$$:
$$U_{2} = \frac{j\omega L}{Z_0 + j\omega L} U_t$$

But as stated, I can't find the relation between angular frequency and phase difference. How do I use the phase difference?

 

[sodper]

I'm stuck here. Does anyone have a suggestion?