Can you use Dirichlet Kernel again?

Calculus Level 4

The Cesàro sum of \( \displaystyle \sum_{n=0}^\infty \cos n \) is equal to \( \dfrac12\).

Is the Cesàro sum \( \displaystyle \sum_{n=0}^\infty \sin n \) also equal to \( \dfrac12\)?

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