the graph of y = sin x and the line y = 1/6 over the interval [0,2 pi]. Where do the two graphs intersect? Give exact answers (no decimals)

the graph of y = sin x and the line y = 1/6 over the interval [0,2 pi]. Where do the two graphs intersect? Give exact answers (no decimals) in radians

$$\small{\text{$ \begin{array}{rcl|rcl}\sin{(x_1)} &=& \frac16 \qquad & \qquad \sin{(x_1)} &=& \sin{ (180\ensurement{^{\circ}} -x_2) } =\frac16 \\&&&\\ x_1 &=& \arcsin{( \frac16 )} \qquad & \qquad \sin{ (180\ensurement{^{\circ}} - x_2) } &=&\frac16 \\&&&\\ x_1 &=& 9.59406822686 \ensurement{^{\circ}} \qquad & \qquad 180\ensurement{^{\circ}} - x_2 &=& \arcsin{( \frac16 )} \\&&&\\x_1 &=& 0.05330037904\cdot \pi = 0.16744807922 \qquad &\qquad x_2 &=& 180\ensurement{^{\circ}}-\arcsin{( \frac16 )} \\ &&&\\ &&\qquad & x_2 &=& 180\ensurement{^{\circ}}-9.59406822686 \ensurement{^{\circ}}\\ &&&\\ &&\qquad & x_2 &=& 170.405931773\ensurement{^{\circ}}\\ &&&\\ &&\qquad & x_2 &=& 0.94669962096\cdot \pi = 2.97414457437 \end{array}$}}$$