Find $\frac{{{\text{d}}y}}{{{\text{d}}\theta }}$

Hence find the values of θ for which $\frac{{{\text{d}}y}}{{{\text{d}}\theta }} = 2y$.

attempt at chain rule or product rule     (M1)

$\frac{{{\text{d}}y}}{{{\text{d}}\theta }} = 2\,{\text{sin}}\,\theta \,{\text{cos}}\,\theta$     A1

[2 marks]

$2\,{\text{sin}}\,\theta \,{\text{cos}}\,\theta  = 2{\text{si}}{{\text{n}}^2}\theta$

sin θ = 0     (A1)

θ = 0, $\pi$     A1

obtaining cos θ = sin θ     (M1)

tan θ = 1     (M1)

$\theta  = \frac{\pi }{4}$     A1

[5 marks]