If a unit vector $\vec { a }$ makes angles $\frac { \pi } { 3 }$ with $\hat { i } , \frac { \pi } { 4 }$ with $\hat { j }$ and $\theta \in ( 0 , \pi )$ with $\widehat { k }$, then a value of $\theta$ is:\\
(1) $\frac { 5 \pi } { 6 }$\\
(2) $\frac { 5 \pi } { 12 }$\\
(3) $\frac { \pi } { 4 }$\\
(4) $\frac { 2 \pi } { 3 }$