Solve `(tan^(2) x+2sqrt(3) tan x+7) (cot^(2) y-2 sqrt(3) cot y+8) le 20` for x and y.

Explanation

To solve the inequality \((\tan^2 x + 2\sqrt{3} \tan x + 7)(\cot^2 y - 2\sqrt{3} \cot y + 8) \leq 20\), we will break it down into manageable steps.

### Step 1: Rewrite the expressions
We can rewrite the expressions in a more manageable form. The first part can be expressed as:
\[ \tan^2 x + 2\sqrt{3} \tan x + 7 = (\tan x + \sqrt{3})^2 + 4 \]
This is because:
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