To solve this equation, we can first simplify it by distributing the 8 to both terms inside the parentheses:

8cosy - 56/siny + 1 = 0

Next, we can move the 56/siny to the other side of the equation by adding it to both sides:

8cosy + 1 = 56/siny

Now, we can get rid of the fraction by multiplying both sides by siny:

siny(8cosy + 1) = 56

Expanding the left side:

8cosy(siny) + siny = 56

Using the trigonometric identity cos(x)sin(x) = 1/2sin(2x), we get:

4sin(2y) + siny = 56

Now, let's rearrange the equation to isolate the siny term:

siny(4cosy + 1) = 56

Finally, we can solve for siny:

siny = 56 / (4cosy + 1)