The problem is to find out the derivative of the given function with respect to other given function.
In this type of problem first give a suitable transformation and then differentiate both function with respect to that transformation and the find the required value.
Here first give a transformation of sine function.
Then differenciate both the given function after substuting the sine function. Then solve it.

Here a complex point is given and we have to find the value of theta where the complex number is purely imaginary.
For such problem 1st convert the complex number into standard form of complex number.
Here 1st convert the given complex into standard form of complex number.
Since the complex number is purely imaginary then its real part must be zero. Equating the real part zero, find the required the value.