Find the equations of the tangent and normal to the curve x = asin³θ and y = acos³θ at θ = π/4.

Let x = asin³θ, y = acos³θ
dxdθ = 3asin²θcosθ
dydθ = -3acos²θsinθ
dydx = -3acos²θsinθ / 3asin²θcosθ = -cotθ
|dydx|θ=π/4 = -1
Equation of tangent at θ = π/4
y - acos³(π/4) = -1(x - asin³(π/4))
y - a/2√2 = -(x - a/2√2)
y + x = a/√2
y + x = a√2
Equation of normal at θ = π/4
y - a/2√2 = 1(x - a/2√2)
Therefore, y - x = 0