Answer
$36.9^{\circ},143.1^{\circ},216.9^{\circ}.323.1^{\circ}$
Work Step by Step
$7\sin^2{\theta} -9(1-2\sin^2{\theta}) = 0$
$7 \sin^2{\theta} + 18 \sin^2{\theta} = 9$
$ 25 \sin^2{\theta} = 9$
$\sin^2{\theta} = \dfrac{9}{25}$
$\sin{\theta}= \pm 0.6$
$\theta = 36.9^{\circ},143.1^{\circ},216.9^{\circ}.323.1^{\circ}$
