Find all triplets $(x,y,z)$ that satisfy:

$${x}^{2012}+{y}^{2012}+{z}^{2012}=3\phantom{\rule{0ex}{0ex}}{x}^{2013}+{y}^{2013}+{z}^{2013}=3\phantom{\rule{0ex}{0ex}}{x}^{2014}+{y}^{2014}+{z}^{2014}=3$$

Trivial solution: $(1,1,1)$

$${x}^{2012}+{y}^{2012}+{z}^{2012}=3\phantom{\rule{0ex}{0ex}}{x}^{2013}+{y}^{2013}+{z}^{2013}=3\phantom{\rule{0ex}{0ex}}{x}^{2014}+{y}^{2014}+{z}^{2014}=3$$

Trivial solution: $(1,1,1)$