For how many positive integers n less than or equal to 1000 is

$$(\sin t+i \cos t)^{n}=\sin n t+i \cos n t$$

true for all real t ?

For how many positive integers n less than or equal to 1000 is

$$(\sin t+i \cos t)^{n}=\sin n t+i \cos n t$$

true for all real t ?