Find the value of $\sin 15^{\circ}$.

  • A
    $\frac{\sqrt{3} - 1}{2\sqrt{2}}$
  • B
    $\frac{\sqrt{3} + 1}{2\sqrt{2}}$
  • C
    $\frac{\sqrt{6} - \sqrt{2}}{4}$
  • D
    $\frac{\sqrt{6} + \sqrt{2}}{4}$

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