To solve this trigonometric equation, we can use the double-angle formula for sine:

2sin(π/4 + a) = √2(sin a + cos a)
2(sin(π/4)cos(a) + cos(π/4)sin(a)) = √2(sin a + cos a)
2(√2/2 cos(a) + √2/2 sin(a)) = √2(sin a + cos a)
cos(a) + sin(a) = sin(a) + cos(a)

Since the left side and right side of the equation are equal, the equation is true for all values of 'a'. So, the solution to this equation is all real numbers.