The Whimsical Cosine

Geometry Level 5

\[\sum_{r=1}^{10} \sec^{4r} \theta=88+\frac {a}{\cos^4 \theta}\]

Given \(\cos^8 \theta+\cos^4 \theta=1.\) and that it satisfy the equation above for some constant \(a\). Find \(a\).


Note: This is one of my original problems. It belongs to the set- Questions I've Made ©.
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