Finding solutions to $ \sin\left(n \pi \frac{T_p}{T}\right) - \sin\left(n \pi \frac{T_0}{T}\right) = \sin\left( \frac{{n \pi}}{2}\right) $

Question

I'm trying to figure out how I can find a solution(s) to the equation below.

$$ \sin\left(n \pi \frac{T_p}{T}\right) - \sin\left(n \pi \frac{T_0}{T}\right) = \sin\left( \frac{{n \pi}}{2}\right) $$

I'm expecting something in the form of $T_p$ and $T_o$ expressed as part of $T$, for example: $T_p = \frac12 T$ and $T_0 = \frac13 T$.

Any hits would be hugely appreciated.

Best, A