Parametric equations and finding tangents from circles

[xllx]

Homework Statement

A circle has the parametric equations:
x=1+2cos\theta
y=3+2sin\theta

dy/dx= -1/tan\theta

Find the tangent equation at the point with parameter \theta

Homework Equations

y-y1=m(x-x1)

The Attempt at a Solution

I've tried putting dy/dx in as the gradient and then x1 and y1 as the parametric equations but i seem to come up with some really long equation that I am sure isn't right.

Any help at all would be greatly appreciated. Many thanks.

 

[Mentallic]

You mean you don't think this is right?:

y-3-2sin\theta=-cot\theta(x-1-2cos\theta)

Because it is