Let
$$\alpha = \sum _ { k = 1 } ^ { \infty } \sin ^ { 2 k } \left( \frac { \pi } { 6 } \right) .$$
Let $g : [ 0,1 ] \rightarrow \mathbb { R }$ be the function defined by
$$g ( x ) = 2 ^ { \alpha x } + 2 ^ { \alpha ( 1 - x ) }$$
Then, which of the following statements is/are TRUE ?
(A) The minimum value of $g ( x )$ is $2 ^ { \frac { 7 } { 6 } }$\\
(B) The maximum value of $g ( x )$ is $1 + 2 ^ { \frac { 1 } { 3 } }$\\
(C) The function $g ( x )$ attains its maximum at more than one point\\
(D) The function $g ( x )$ attains its minimum at more than one point