Trigonometry (3)

Geometry Level 4

If \[\large 2008=2^{a_1}+2^{a_2}+\cdots+2^{a_n}\] where \(a_1\), \(a_2\), \(\cdots\), \(a_n\) are distinct non-negative integers, let \[x=\sin\sum_{i=1}^na_i\] \[y=\cos\sum_{i=1}^na_i\] \[z=\tan\sum_{i=1}^na_i\] Compare the sizes of \(x\), \(y\) and \(z\).

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