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` vec a , vec ba n d vec c` are unit vectors such that `| vec a+ vec b+3 vec c|=4.` Angle between ` vec aa n d vec bi stheta_1,` between ` vec ba n d vec c` is `theta_2` and between ` vec aa n d vec c` varies `[pi//6,2pi//3]dot` Then the maximum of `costheta_1+3costheta_2i s` `3` b. `4` c. `2sqrt(2)` d. `6`

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