How do I solve this? My work has led me to a dead end.

Question

tan(45-x) + cot(45-x) =4

my work:
(tan45 - tanx)/(1+ tan45tanx) + (cot45 - cotx)/(1 + cot45cotx) = 4

(1-tanx)/(1+tanx) + (1-cotx)/(1+cotx) = 4

Then I found a common denominator, giving me this:
(2-2cotxtanx)/(1+cotx+tanx+cotxtanx) =4
I can't cancel the cotxtanx's because they're in the middle of a term, right? So where do I go from here? Or did I make a mistake somewhere?

This is how I would soleve it. First put 45 - x = y. Then:

Sin(y)/Cos(y) + Cos(y)/Sin(y) = 4 -->

[Sin^2(y) + Cos^2(y)]/(Sin(y)Cos(y)) = 4

1/(Sin(y)Cos(y)) = 4 --->

Sin(2y) = 1/2