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Let $m$ be an even integer greater than $8$. Is there any software I can use to determine for some small $m$ whether the following constraints on $t_0,\ldots,t_{m-1}$ and $w$ have solutions?

$-\pi\leq t_r\leq\pi,\ r=0,\ldots,m-1,$

$0\leq w\leq\frac{1}{m},$

$\sum\limits_{j=1}^{2r-1}\cos(t_j+t_{2r-j})+\sum\limits_{j=2r+1}^{m-1}\cos(t_j+t_{2r+m-j})=w\cos \sum\limits_{j=1}^{2r-1}\cos(t_j+t_{2r-j})+\sum\limits_{j=2r+1}^{m-1}\cos(t_j+t_{2r+m-j})=2w\cos t_{2r},\ r=1,\ldots,\frac{m}{2}-1,$

$\sum\limits_{j=1}^{2r-1}\sin(t_j+t_{2r-j})+\sum\limits_{j=2r+1}^{m-1}\sin(t_j+t_{2r+m-j})=w\sin \sum\limits_{j=1}^{2r-1}\sin(t_j+t_{2r-j})+\sum\limits_{j=2r+1}^{m-1}\sin(t_j+t_{2r+m-j})=2w\sin t_{2r},\ r=1,\ldots,\frac{m}{2}-1,$

$t_r+t_{m-r}=0,\ r=1,\ldots,\frac{m}{2},$

$\cos(t_r+t_{\frac{m}{2}+r})=\cos(t_{2r}+rt_0),\ r=1,\ldots,\frac{m}{2}-1,$

$\sin(t_r+t_{\frac{m}{2}+r})=\sin(t_{2r}+rt_0),\ r=1,\ldots,\frac{m}{2}-1,$

$\cos(\frac{mt_0}{2})=1.$

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Let $m$ be an even integer greater than $8$. Is there any software I can use to determine for some small $m$ whether the following constraints on $t_0,\ldots,t_{m-1}$ and $w$ have solutions?

$-\pi\leq t_r\leq\pi,\ r=0,\ldots,m-1,$

$0\leq w\leq\frac{1}{m},$

$\sum\limits_{j=1}^{2r-1}\cos(t_j+t_{2r-j})+\sum\limits_{j=2r+1}^{m}\cos(t_j+t_{2r+m-j})=w\cos \sum\limits_{j=1}^{2r-1}\cos(t_j+t_{2r-j})+\sum\limits_{j=2r+1}^{m-1}\cos(t_j+t_{2r+m-j})=w\cos t_{2r},\ r=1,\ldots,\frac{m}{2}-1,$

$\sum\limits_{j=1}^{2r-1}\sin(t_j+t_{2r-j})+\sum\limits_{j=2r+1}^{m}\sin(t_j+t_{2r+m-j})=w\sin \sum\limits_{j=1}^{2r-1}\sin(t_j+t_{2r-j})+\sum\limits_{j=2r+1}^{m-1}\sin(t_j+t_{2r+m-j})=w\sin t_{2r},\ r=1,\ldots,\frac{m}{2}-1,$

$t_r+t_{m-r}=0,\ r=1,\ldots,\frac{m}{2},$

$\cos(t_r+t_{\frac{m}{2}+r})=\cos(t_{2r}+rt_0),\ r=1,\ldots,\frac{m}{2}-1,$

$\sin(t_r+t_{\frac{m}{2}+r})=\sin(t_{2r}+rt_0),\ r=1,\ldots,\frac{m}{2}-1,$

$\cos(\frac{mt_0}{2})=1.$

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Let $m$ be an even integer greater than $8$. Is there any software I can use to determine for some small $m$ whether the following constraints on $t_0,\ldots,t_{m-1}$ and $w$ have solutions?

$-\pi\leq t_r\leq\pi,\ r=0,\ldots,m-1,$

$0 0\leq w\leq\frac{1}{m},$

$\sum\limits_{j=1}^{2r-1}\cos(t_j+t_{2r-j})+\sum\limits_{j=2r+1}^{m}\cos(t_j+t_{2r+m-j})=w\cos t_{2r},\ r=1,\ldots,\frac{m}{2}-1,$

$\sum\limits_{j=1}^{2r-1}\sin(t_j+t_{2r-j})+\sum\limits_{j=2r+1}^{m}\sin(t_j+t_{2r+m-j})=w\sin t_{2r},\ r=1,\ldots,\frac{m}{2}-1,$

$t_r+t_{m-r}=0,\ r=1,\ldots,\frac{m}{2},$

$\cos(t_r+t_{\frac{m}{2}+r})=\cos(t_{2r}+rt_0),\ r=1,\ldots,\frac{m}{2}-1,$

$\sin(t_r+t_{\frac{m}{2}+r})=\sin(t_{2r}+rt_0),\ r=1,\ldots,\frac{m}{2}-1,$

$\cos(\frac{mt_0}{2})=1.$

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