#### Question

If \theta \in [0,2\pi], find the maximum value of

f = |\sin^2 \theta {\sin^3(2\theta )\cdotp \sin^3 (4\theta ) \dots\sin^3 (2^{n-1} }\sin (2^n\theta )|

If \theta \in [0,2\pi], find the maximum value of

f = |\sin^2 \theta {\sin^3(2\theta )\cdotp \sin^3 (4\theta ) \dots\sin^3 (2^{n-1} }\sin (2^n\theta )|