On the coordinate plane, let $\theta _ { 1 }$ be the acute angle that the line $y = m x ( 0 < m < \sqrt { 3 } )$ makes with the $x$-axis, and let $\theta _ { 2 }$ be the acute angle that the line $y = m x$ makes with the line $y = \sqrt { 3 } x$. What is the value of $m$ that maximizes $3 \sin \theta _ { 1 } + 4 \sin \theta _ { 2 }$? [4 points] (1) $\frac { \sqrt { 3 } } { 6 }$ (2) $\frac { \sqrt { 3 } } { 7 }$ (3) $\frac { \sqrt { 3 } } { 8 }$ (4) $\frac { \sqrt { 3 } } { 9 }$ (5) $\frac { \sqrt { 3 } } { 10 }$
On the coordinate plane, let $\theta _ { 1 }$ be the acute angle that the line $y = m x ( 0 < m < \sqrt { 3 } )$ makes with the $x$-axis, and let $\theta _ { 2 }$ be the acute angle that the line $y = m x$ makes with the line $y = \sqrt { 3 } x$. What is the value of $m$ that maximizes $3 \sin \theta _ { 1 } + 4 \sin \theta _ { 2 }$? [4 points]\\
(1) $\frac { \sqrt { 3 } } { 6 }$\\
(2) $\frac { \sqrt { 3 } } { 7 }$\\
(3) $\frac { \sqrt { 3 } } { 8 }$\\
(4) $\frac { \sqrt { 3 } } { 9 }$\\
(5) $\frac { \sqrt { 3 } } { 10 }$