How can I use sigma index notation to formlate an equation combining the discrete series of trigonometric functions?

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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?