Transfer function of electrical network

A quick look at the fast analytical techniques or FACTs gives you the transfer function of this guy in the blink of an eye. First, turn the stimulus off or reduce \$V_{in}\$ to 0 V: replace the source by a short circuit. Then, "look" through the capacitor terminals to determine resistance \$R\$ between the terminals. It's immediate: \$R=R+R=2R\$. You have the natural time constant equal to \$\tau=2RC\$ and the pole in a first-order system is the inverse of the time constant: \$\omega_p=\frac{1}{2RC}\$.

For the zero, you have to check what condition in this circuit would make the ac response to 0 V despite the presence of a stimulus? Well, if the series combination of \$R\$ and \$C\$ would lead to a transformed short, then the output would be 0 V. Just solve \$Z(s)=R+\frac{1}{sC}=0\$ and you find a root at \$s_z=-\frac{1}{RC}\$ and a zero located at \$\omega_z=\frac{1}{RC}\$. The below drawing shows the approach:

A quick Mathcad sheet shows the response of this filter where the pole is below the zero by a ratio of 2:

how should i calculate size and angle

Here's a decent clue for the magnitude of the bode plot: -