If \(\frac{{{a^z}}}{{b\; + \;c}} = \frac{{{b^z}}}{{c\; + \;a}} = \frac{{{c^z}}}{{a\; + \;b}} = 1\) then find the value of \(\frac{2}{{1\; + \;a}}\; + \;\frac{2}{{1\; + \;b}}\; + \;\frac{2}{{1\; + \;c}}\)
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If \(\frac{{{a^z}}}{{b\; + \;c}} = \frac{{{b^z}}}{{c\; + \;a}} = \frac{{{c^z}}}{{a\; + \;b}} = 1\) then find the value of \(\frac{2}{{1\; + \;a}}\; + \;\frac{2}{{1\; + \;b}}\; + \;\frac{2}{{1\; + \;c}}\)