How can I use sigma index notation to formulate an equation combining the discrete series of trigonometric functions?
For $n = 1$: $f=\sin (\pi-\theta_1)$
For $n = 2$: $f=\sin (\pi-\theta_1) + \sin (2\pi-(\theta_1 + \theta_2))$
For $n = 3$: $f=\sin (\pi-\theta_1) + \sin (2\pi-(\theta_1 + \theta_2)) + \sin (3\pi-(\theta_1 + \theta_2 + \theta_3))$
Attempt:
For an arbitrary value of $n$, where 1 < n < 3: $$f = \sum_{1}^{n} \sin(i\cdot\pi−\theta_i)$$
Help me correct the equation please?