Fill in the blanks below appropriately to obtain a proof for the expression

Proof:

$(1 + \tan(A) + \sec(A) ) \cdot (1 + \cot(A)-\csc(A) )$

$\hspace{10mm} = 1 + \cot(A) - \csc(A) + \tan(A) + \tan(A)\cot(A) - \tan(A)\csc(A) + \sec(A) + \sec(A)\cot(A) - \sec(A)\csc(A)$

$\hspace{10mm} = \tan(A) +$ $- \sec(A)\cdot$ $+ \; 2$

$\hspace{10mm} =$ $/ \cos(A) +$ $/ \sin(A) - 1 / ( \sin(A) \cdot$ $) + \; 2$

$\hspace{10mm} =$ $/ \left ( \sin(A) \cdot \cos(A) \right ) -$ $/ \left [ \sin(A) \cos(A) \right ] + \; 2$

$\hspace{10mm} =$ $/ \left [ \sin(A) \cdot \cos(A) \right ] + \; 2$

$\hspace{10mm} = 2$

Your goal is to fill in the blanks with appropriate formulas to make adjacent expressions equal.
There may be other ways to prove the original identity but this problem requires the correct logic using this approach.

Hint: At each step, look to see which terms might cancel or combine.