A geometry problem by Archit Tripathi

Geometry Level 5

The value of

\[\sum_{r=0}^6 {6\choose r} \sin(r + 1)x\]

is equal to \((2\cos(\frac{x}{2}))^{p}\sin(q + 1)x\).

Find the value of \(\frac{25(p + q)}{3}\).

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