`cot alpha = 1/2, sec beta = -5/3`
As alpha lies between `pi and (3pi)/2`, only `tan alpha and cot alpha` will be positive.
As beta lies between `pi/2 and pi`, only `sin beta and cosec beta` will be positive. Rest of the trigonometric functions will be negative.
Now, `cot alpha = 1/2, sec beta = -5/3`
`=> tan alpha = 2, tan beta = -(sqrt((5/3)^2-1)) = -4/3`
`:. tan alpha = 2 and tan beta = -4/3`
Now, `tan(alpha+beta) = (tan alpha+tan beta)/(1-tanalphatanbta)`
`=(2-4/3)/(1-2(-4/3))`
`=(2/3)/(11/3) = 2/11`
`:. tan(alpha+beta) = 2/11`
`:. alpha+beta = tan^-1(2/11).`
