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If a unit vectorvec(a) makes angle (pi)/...

If a unit vector`vec(a)` makes angle `(pi)/(3)` with `hat(i), (pi)/(4)` with `hat(j)` and `theta in ((pi)/(2), pi)` with `hat(k)` then a value of `theta` is `(k pi)/(l)` (k and l are coprime). The value of k is _________.

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