Too Complex! Part- IV

Geometry Level 5

If sin 7θ can be expressed as follows-

\( sin 7θ = 64 sin θ (sin^{2}p - sin^{2}θ)(sin^{2}q - sin^{2}θ)(sin^{2}r - sin^{2}θ)\)

Find p + q + r.

\(\textbf{NOTE-}\)

p,q and r are distinct real numbers in the interval \( (0,\frac{\pi}{2})\)

\(\textbf{CLUE-}\)

Use \(z^{14} -1 = 0\)

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