Algebra + trigo problems

Geometry Level 3

If \({ a }_{ k } > 0\) such that \(\sum _{ 1 }^{ 2015 }{ { a }_{ k } } \quad =\quad 1\)

Let \(E = \sum _{ 1 }^{ 2015 }{ { { a }_{ k } }^{ 2 } }\).

Let the minimum value of \(E\) be \(x\).

Find the value of \(\sin { (120900x) } -\cos { (60450x) } = ?\)

Note: assume that angles are in degrees.

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