Intersection b is perpendicular to CD, and the extension line of intersection CD is at point e,

Because angle e = angle ACD = 90 degrees, angle EDB= = angle CDA,

Ad = BD, so all triangles EDB are equal to CDA. ..

So AC = be, BC = 2be, because the angle BCD=30 degrees.

Let be = x, then BC = 2x, CE = root 3X,

Cd = root 3X, AC = x,

The root of ad = 2 7x,

So the sine value of the angle CDA =AC/AD=X/2 root 7x = 2 times of 7.

Root number 7, cosine value of angle CDA = 2 of root number 3X/2/ 2 of root number 7X=7 = 7 of root number 2 1.