Trigonometry Identity

Level pending

Given the following trigonometry equation:

\[\displaystyle \cot^4 11.25^\circ + \cot^4 22.5^\circ + \cot^4 33.75^\circ + \tan^4 11.25^\circ + \tan^4 22.5^\circ + \tan^4 33.75^\circ = N\]

Find the value of \(\displaystyle N\) where \(\displaystyle N\) is a positive integer.

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