Given, x = a(cos⁡θ+ θ sin⁡θ )

Differentiate w.r.t. θ, we get

dx/dθ = a(-sin⁡θ + sin⁡θ + θ cosθ )

 and

y = a(sin⁡θ - θ cos⁡θ )

dy/dθ = a(cos⁡θ - cos⁡θ + θ sinθ )

Now, dy/dx = (dy/dθ)/(dx/dθ)

=> dy/dx = (a(cos⁡θ - cos⁡θ + θ sinθ ) )/(-sin⁡θ + sin⁡θ + θ cosθ )

=> dy/dx = (θ sinθ )/(θ cosθ )

=> dy/dx = tanθ

Now, (dy/dx)_{x = π/4} = tan π/4

=> (dy/dx)_{x = π/4} = 1