So the tangent chord on the left is diagonally multiplied.

sinc cosa-cosc Sina = cosc sinb-sinc cosb，

So sin(C-A)=sin(B-C).

So C-A=B-C or C-A= pai -(B-C) (invalid).

That is 2C=A+B, C=60 degrees,

So A+B= 120 degrees,

And because sin(B-A)=cosC= 1/2,

So B-A=30 degrees or B-A= 150 degrees,

So A=45 degrees.

(2). Triangle area =1/2 * ac * sinb = (square root of 6+radical number 2)/8*ac=3+ radical number 3,

And a/sinA=c/sinC,

So a=2 times the root number 2, and c=2 times the root number 3.