>>615
det(A)
=1+cxcycc(x+y)+cxcycc(x+y)-c(x+y)^2-cx^2-cy^2
=1+2cxcy(cxcy-sxsy)-(cxcy-sxsy)^2-cx^2-cy^2
=1+(cxcy)^2-(sxsy)^2-cx^2-cy^2
=1+(cxcy)^2-(1-cx^2)(1-cy^2)-cx^2-cy^2
=1+(cxcy)^2-1-cx^2cy^2+cx^2+cy^2-cx^2-cy^2
=0