If sinθ = 8/15 , then what is the value of tanθ + cotθ ?

sinθ =  \(\frac{8}{15}\)

⇒ sinθ = \(\frac{8(P)}{15(H)}\)

using Pythagoras theorem , 

Base = 17

tanθ + cotθ  = \(\frac{P}{B}\)  +  \(\frac{B}{P}\) 

= \(\frac{8}{17}\)  + \(\frac{17}{8}\)   

= \(\frac{353}{136}\)