(a) Show that 3sin3θ−4cos3θ can be written in the form Rsin(3θ−α), with R>0 and 0<α<90°.

(b) Deduce the minimum value of 3sin3θ−4cos3θ and work out the smallest positive value of θ (to the nearest 0.1°) at which it occurs.

I did the first part and got $\displaystyle 5sin( 3\theta-53.1) $

but how do I find the minimum value? I have set it equal to 0, but that does not give me the correct answer.

can someone please tell me

?

Thanks!