Find the exact value of the expression. Do not use a calculator.
[ cot 45⁰ - sin 45⁰ ( 2 - √2/2 ) ( 2 - √3/2 - √3/6 ) ( 2√3 - 3√2/6 ) ]
a) (-1/2)
b) (1/2)
c) (√2/2)
d) (√2)