If $a\,{\cos ^3}\alpha + 3a\,\cos \alpha \,{\sin ^2}\alpha = m$ and $a\,{\sin ^3}\alpha + 3a\,{\cos ^2}\alpha \sin \alpha = n,$ then  ${(m + n)^{2/3}} + {(m - n)^{2/3}}$ is equal to

  • A

    $2{a^2}$

  • B

    $2{a^{1/3}}$

  • C

    $2{a^{2/3}}$

  • D

    $2{a^3}$

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