Given, sin(π*2cos θ) = cos(π*2sin θ)

=> sin(π*2cos θ) = sin{π/2 - (π*2sin θ)}

=> π*2cos θ = π/2 - (π*2sin θ)

=> π*2cos θ + π*2sin θ = π/2

=> cos θ + sin θ = (π/2)/(2π)

=> cos θ + sin θ = 1/4

=> (1/√2)*cos θ + (1/√2)*sin θ = (1/4)*(1/√2)    {MULTIPLY BOTH SIDE BY 1/√2}

=> sin π/4 * cos θ + cos π/4 *sin θ = 1/4√2          {since sin π/4 = cos π/4 = 1/√2}

=> sin(θ + π/4) = (1/4)*sin π/4                             {using sin(a + b) formula}