sin(x)*cos(2*y)=3/4 cos(x)*sin(2*y)=3/4

$$sin{left (x right )} cos{left (2 y right )} = frac{3}{4}$$

cos(x)*sin(2*y) = 3/4

$$sin{left (2 y right )} cos{left (x right )} = frac{3}{4}$$

$$x_{1} = pi – {asin}{left (frac{3}{4 cos{left (2 {atan}{left (- frac{2}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} + frac{sqrt{5} i}{3} right )} right )}} right )}$$
=
$$pi – {asin}{left (frac{3}{4 cos{left (2 {atan}{left (- frac{2}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} + frac{sqrt{5} i}{3} right )} right )}} right )}$$
=

2.35619449019234 – 0.481211825059603*i

$$y_{1} = – {atan}{left (- frac{2}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} + frac{sqrt{5} i}{3} right )}$$
=
$$- {atan}{left (- frac{2}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} + frac{sqrt{5} i}{3} right )}$$
=

-0.392699081698724 – 0.240605912529802*i

$$x_{2} = pi – {asin}{left (frac{3}{4 cos{left (2 {atan}{left (frac{2}{3} – frac{sqrt{5} i}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} right )} right )}} right )}$$
=
$$pi – {asin}{left (frac{3}{4 cos{left (2 {atan}{left (frac{2}{3} – frac{sqrt{5} i}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} right )} right )}} right )}$$
=

3.92699081698724 + 0.481211825059603*i

$$y_{2} = – {atan}{left (frac{2}{3} – frac{sqrt{5} i}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} right )}$$
=
$$- {atan}{left (frac{2}{3} – frac{sqrt{5} i}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} right )}$$
=

-1.17809724509617 + 0.240605912529802*i

$$x_{3} = pi – {asin}{left (frac{3}{4 cos{left (2 {atan}{left (frac{2}{3} – frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )} right )}} right )}$$
=
$$pi – {asin}{left (frac{3}{4 cos{left (2 {atan}{left (frac{2}{3} – frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )} right )}} right )}$$
=

2.35619449019234 + 0.481211825059603*i

$$y_{3} = {atan}{left (frac{2}{3} – frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )}$$
=
$${atan}{left (frac{2}{3} – frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )}$$
=

-0.392699081698724 + 0.240605912529802*i

$$x_{4} = pi – {asin}{left (frac{3}{4 cos{left (2 {atan}{left (frac{2}{3} + frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )} right )}} right )}$$
=
$$pi – {asin}{left (frac{3}{4 cos{left (2 {atan}{left (frac{2}{3} + frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )} right )}} right )}$$
=

3.92699081698724 – 0.481211825059603*i

$$y_{4} = – {atan}{left (frac{2}{3} + frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )}$$
=
$$- {atan}{left (frac{2}{3} + frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )}$$
=

-1.17809724509617 – 0.240605912529802*i

$$x_{5} = {asin}{left (frac{3}{4 cos{left (2 {atan}{left (- frac{2}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} + frac{sqrt{5} i}{3} right )} right )}} right )}$$
=
$${asin}{left (frac{3}{4 cos{left (2 {atan}{left (- frac{2}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} + frac{sqrt{5} i}{3} right )} right )}} right )}$$
=

0.785398163397448 + 0.481211825059603*i

$$y_{5} = {atan}{left (- frac{2}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} + frac{sqrt{5} i}{3} right )}$$
=
$${atan}{left (- frac{2}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} + frac{sqrt{5} i}{3} right )}$$
=

0.392699081698724 + 0.240605912529802*i

$$x_{6} = {asin}{left (frac{3}{4 cos{left (2 {atan}{left (frac{2}{3} – frac{sqrt{5} i}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} right )} right )}} right )}$$
=
$${asin}{left (frac{3}{4 cos{left (2 {atan}{left (frac{2}{3} – frac{sqrt{5} i}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} right )} right )}} right )}$$
=

-0.785398163397448 – 0.481211825059603*i

$$y_{6} = {atan}{left (frac{2}{3} – frac{sqrt{5} i}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} right )}$$
=
$${atan}{left (frac{2}{3} – frac{sqrt{5} i}{3} + frac{2}{3} sqrt{2 – sqrt{5} i} right )}$$
=

1.17809724509617 – 0.240605912529802*i

$$x_{7} = {asin}{left (frac{3}{4 cos{left (2 {atan}{left (frac{2}{3} – frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )} right )}} right )}$$
=
$${asin}{left (frac{3}{4 cos{left (2 {atan}{left (frac{2}{3} – frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )} right )}} right )}$$
=

0.785398163397448 – 0.481211825059603*i

$$y_{7} = – {atan}{left (frac{2}{3} – frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )}$$
=
$$- {atan}{left (frac{2}{3} – frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )}$$
=

0.392699081698724 – 0.240605912529802*i

$$x_{8} = {asin}{left (frac{3}{4 cos{left (2 {atan}{left (frac{2}{3} + frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )} right )}} right )}$$
=
$${asin}{left (frac{3}{4 cos{left (2 {atan}{left (frac{2}{3} + frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )} right )}} right )}$$
=

-0.785398163397448 + 0.481211825059603*i

$$y_{8} = {atan}{left (frac{2}{3} + frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )}$$
=
$${atan}{left (frac{2}{3} + frac{2}{3} sqrt{2 + sqrt{5} i} + frac{sqrt{5} i}{3} right )}$$
=

1.17809724509617 + 0.240605912529802*i