this equation becomes very easy one, if you just write it like this:
(a+b)(c-d)=(a-b)(c+d), and need to prove a/b=c/d
here a=sin65
b=cos67
c=sin40
d=cos33
from (a+b)(c-d)=(a-b)(c+d) we'll get
ac-ad+bc-bd=ac+ad-bc-bd
bc-ad=ad-bc
2bc=2ad
bc=ad
ad=bc
a/b=c/d
