The curve with parametric equations along with the tangent at the point with parameter t = 1

find the equation if this tangent and the coordinates of the point where it meets the curve again.

when t = 1

equation of tangent =

however to find the coordinates of where the curve crosses the tangent again, would I not just be able to sub in the values of x and y into the tnagent equation?

can't seem to solve from here,

any help appreicated.

thanks