Which of the following is true for all possible non-zero choices of integers $m,n;m\neq n$, or all possible non-zero choices of real numbers $p,q;p\neq q$, as applicable?
1. $\frac{1}{\pi}\int_{0}^{\pi}\sin m\theta \sin n\theta d\theta = 0$
2. $\frac{1}{2\pi}\int_{-\pi/2}^{\pi /2}\sin p\theta \sin q\theta d\theta = 0$
3. $\frac{1}{2\pi}\int_{-\pi}^{\pi}\sin p\theta \cos q\theta d\theta = 0$
4. $\displaystyle \lim_{\alpha\rightarrow \infty }\frac{1}{2\alpha }\int_{-\alpha }^{\alpha }\sin p\theta \sin q\theta d\theta = 0$