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Solution:

tan ( a + pi/3)

= tan [(a + b) - (b - pi/3)]

Using the formula: tan (x - y) = (tan x - tan y)/(1 + tan x tan y)

tan [(a + b) - (b - pi/3)]

= [tan (a + b) - tan (b - pi/3)]/[ 1 + tan (a + b) tan (b - pi/3)]

= (1/3 - 1/5)/[1 + (1/3) (1/5)]

= [(1 × 5)/(3 × 5) - (1 × 3)/(5 × 3)/[1 + (1/3) (1/5)]

= (5 - 3)/15 ÷ (15/15 + 1/15)

= 2/15 ÷ 16/15

= 2/15 × 15/16

= 2/16

= 1/8

Therefore, the value of tan ( a + pi/3) is 1/8. Watch the video for more details.