Let set ‘X’ be the set of first 100 natural numbers i.e. X = {1, 2, 3, ..,, 100} and set Y be a subset of set ‘X’, such that 
$Y=\{a_1,a_2,a_3,\mathrm{.......},a_n\},$

$\hspace{0.17em}where{a}_i+a_j\ne 7k\forall i\ne j(k\in \mathbb{Z})$
$If\lambda =\alpha \tan {108}^0+\beta \tan 8^0$  is a real number satisfying 
$\lambda =\frac{\tan 8^0}{1-3{\tan }^2{8}^0}+\frac{3\tan {24}^0}{1-3{\tan }^2{24}^0}+\frac{9\tan {72}^0}{1-3{\tan }^2{72}^0}+\frac{27\tan {216}^0}{1-3{\tan }^2{216}^0}$
Then the value of $\alpha +\beta +\max \left|Y\right|$  is equal to (|A| denotes cardinality of set A)