fs=Nμ
fs=mgμ→ maximum value of friction possible
Now R= resultant of N&fs
Now, value of fs keeps on increasing and it is equal to the external force f until
f=fs
after that friction force is constantly mgμ
So R increases gradually
R=√(mgμ)2+(mg)2
R=mg√μ2+1→ maximum value of R
Now tanθ=fsN⇒tanθ=mgclmg
⇒tanθ=μ
θ (maximum value of θ) =tan−1(μ)