Can this system of equations have unique solutions?

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I have the equation:

$$c=z[\sin(x)\sin(2\pi yt)-\cos(x)\cos(2\pi yt)]$$

Where $c$ has three known values, each of which is followed by a value for $t$. Therefore one can be left with a system of three equations with three unknowns. Can this system have unique values ?

In other words, can the system:

$$c_1=z[\sin(x)\sin(2\pi yt_2)-\cos(x)\cos(2\pi yt_2)]$$

$$c_3=z[\sin(x\sin(2\pi yt_3)-\cos(x)\cos(2\pi yt_3)]$$

Where $c_1,c_2,c_3,t_1,t_2,t_3$ are all known be solved with unique solutions ?

The values can be obtained with the help of a computer, no need to solve it manually, just want to know if it has unique solutions

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If the system has solutions, they are non-unique since $\cos x$ and $\sin x$ are periodic, so if $x$ is a solution, so is $x+2k\pi,k\in\Bbb Z$.