=2sin(x-π/4)

The right side of the equation = 3 (siny) 2-6 siny+5.

=3(siny- 1)^2+2

The maximum value on the left side of the equation is 2, and the minimum value on the right side is 2, so when both sides are equal to 2, the equation holds, so:

sin(x-π/4)= 1

siny= 1

Because x, y ∈ (0 0,2 π)

x=3π/4

y=π/2

So: x+y=5π/4.