First find point of contact!

A curve is parametrically represented as

$\begin{cases} x = \cos t+\ln \left(\tan\frac{t}{2}\right) \\ y = \sin t, \end{cases}$

where $t$ is a parameter.

Find the length of tangent to the curve at the point where its $x$ -coordinate is equal to its $y$ -coordinate.

The length of tangent is defined as the distance between the point of contact with the curve and the point where the tangent meets the $x$ -axis.